Symmetry and shape
According to Felix Klein, geometry is the study of those properties of a space that are invariant under the action of a group of transformations. In Riemannian geometry the group of transformations of the space is called the isometry group, although the space can sometimes have additional properties arising from mathematical or physical requirements that also need to be preserved by the transformation group. This is the case of a submanifold, whose geometry is influenced by the structure of the ambient space.
Intuitively, symmetry is the correspondence of shape at each point of a space. An important problem in geometry and in several physical sciences is to determine the symmetries of a space in terms of its shape. Submanifolds that are invariant under the isometries of the ambient manifold are called extrinsically homogeneous, or just homogeneous when there is no possibility of confusion. The main idea of my research project is to classify homogeneous submanifolds of a given Riemannian manifold, study the geometric properties of homogeneous submanifolds, and determine whether their shape is characteristic of them.
Funding
This topic of research has been funded by the following fellowships and projects:
- Simetría, curvatura y ecuaciones geométricas (Symmetry, curvature and geometric equations), Agencia Estatal de Investigación PID2019-105138GB-C21 (Spain) (62920 euro), - . Principal investigator: José Carlos Díaz Ramos, Eduardo García Río.
- Simetría, curvatura y ecuaciones diferenciales en geometría (Symmetry, curvature and differential equations in geometry), Agencia Estatal de Investigación MTM2016-75897-P (Spain) (72963 euro), - . Principal investigator: José Carlos Díaz Ramos, Eduardo García Río.
- Homoxeneidade e curvatura de variedades e subvariedades (Homogeneity and curvature of manifolds and submanifolds), Galician government ED431F 2017/03 (Spain) (40000 euro), - . Principal investigator: José Carlos Díaz Ramos.
- Simetría, homogeneidad y curvatura (Symmetry, homogeneity and curvature), Galician government EM2014/009 (Spain) (93000 euro), - . Principal investigator: José Carlos Díaz Ramos.
- Simetría, curvatura y rigidez de estructuras geométricas (Symmetry, curvature and rigidity of geometric structures), Ministry of Science and Innovation MTM2013-41335-P (Spain) (47700 euro), - . Principal investigator: José Carlos Díaz Ramos, Eduardo García Río.
- Isometric actions, European Commission PERG04-GA-2008-239162 (45000 euro), - . Principal investigator: José Carlos Díaz Ramos.
- Symmetry and shape, European Commission MEIF-CT-2006-038754 (147640.42 euro), - . Principal investigator: Jürgen Berndt.
Advisorship of students
I have been advisor of the following Ph.D. students:
- Alberto Rodríguez Vázquez: Homogeneous hypersurfaces and totally geodesic submanifolds, Ph.D. thesis, University of Santiago de Compostela, .
- Olga Pérez Barral: Ruled hypersurfaces and homogeneous submanifolds in semi-Riemannian manifolds, Ph.D. thesis, University of Santiago de Compostela, .
- Víctor Sanmartín López: Homogeneous submanifolds and isoparametric hypersurfaces in symmetric spaces of noncompact type, Ph.D. thesis, University of Santiago de Compostela, .
- Cristina Vidal Castiñeira: Submanifolds in complex projective and hyperbolic planes, Ph.D. thesis, University of Santiago de Compostela, .
- Mohammad Javad Vanaei: Cohomogeneity one Lorentzian Manifolds of Constant Curvature, Ph.D. thesis, Tarbiat Modares University, .
- Miguel Domínguez Vázquez: Isoparametric foliations and polar actions on complex space forms, Ph.D. thesis, University of Santiago de Compostela, .
I have also been advisor of the following research works:
- Juan Manuel Lorenzo Naveiro: Homogeneous polar foliations in symmetric spaces (Foliaciones polares homogéneas en espacios simétricos), master thesis, University of Santiago de Compostela, .
- Alberto Rodríguez Vázquez: Hipersuperficies con curvaturas principais constantes en variedades Kähler con curvatura seccional holomorfa constante (Hypersurfaces with constant principal curvatures in Kähler manifolds of constant holomorphic sectional curvature), master thesis, University of Santiago de Compostela, .
- Olga Pérez Barral: Acciones isométricas en el espacio-tiempo de Minkowski (Isometric actions on Minkowski spacetimes), master thesis, University of Santiago de Compostela, .
- Víctor Sanmartín López: Hipersuperficies isoparamétricas en el espacio hiperbólico complejo (Isoparametric hypersurfaces in the complex hyperbolic space), master thesis, University of Santiago de Compostela, .
- Cristina Vidal Castiñeira: Hipersuperficies reais con dúas curvaturas principais nos planos proxectivo e hiperbólico complexos (Real hypersurfaces with two principal curvatures in complex projective and hyperbolic planes), master thesis, University of Santiago de Compostela, .
- Miguel Domínguez Vázquez: Hipersuperficies con curvaturas principais constantes nos espazos proxectivo e hiperbólico complexos (Hypersurfaces with constant principal curvatures in complex projective and hyperbolic spaces), DEA, University of Santiago de Compostela, .
Publications
A list of publications related to this research project is presented below. For a whole list of my publications (with the pdf of some of my papers) click here.
Research papers
- J. C. Díaz-Ramos, J. M. Lorenzo-Naveiro: Codimension two polar homogeneous foliations on symmetric spaces of noncompact type, arXiv:2302.08339 [math.DG].
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, T. Otero-Casal: Cohomogeneity one actions on symmetric spaces of noncompact type and higher rank, to appear in Adv. Math.
- M. Domínguez-Vázquez, V. Sanmartín-López: Isoparametric hypersurfaces in symmetric spaces of non-compact type and higher rank, arXiv:2109.03850 [math.DG].
- J. Berndt, V. Sanmartín-López: Submanifolds with constant principal curvatures in Riemannian symmetric spaces, to appear in Comm. Anal. Geom.
- A. Rodríguez-Vázquez, C. Olmos: Hopf fibrations and totally geodesic submanifolds, arXiv:2302.11711 [math.DG].
- A. Rodríguez-Vázquez: Totally geodesic submanifolds in products of rank one symmetric spaces, arXiv:2205.14720 [math.DG].
- A. Rodríguez-Vázquez, A. Kollross: Totally geodesic submanifolds in exceptional symmetric spaces, to appear in Adv. Math.
- J. M. Lorenzo-Naveiro, I. Solonenko: Sections of polar actions, arXiv:2111.05280 [math.DG].
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, O. Pérez-Barral: Homogeneous CR submanifolds of complex hyperbolic spaces, Publ. Mat. 67 (2023), 891-912.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, T. Hashinaga: Homogeneous Lagrangian foliations on complex space forms, Proc. Amer. Math. Soc. 151 (2023), 823-833.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, A. Rodríguez-Vázquez: Homogeneous and inhomogeneous isoparametric hypersurfaces in rank one symmetric spaces, J. Reine Angew. Math. 779 (2021), 189-222.
- M. Domínguez-Vázquez, O. Pérez-Barral: Existence and uniqueness of inhomogeneous ruled hypersurfaces with shape operator of constant norm in the complex hyperbolic space, Internat. J. Math. 32 (2021), 2150049, 4 pp.
- M. Domínguez-Vázquez, V. Sanmartín-López, H. Tamaru: Codimension one Ricci soliton subgroups of solvable Iwasawa groups, J. Math. Pures Appl. 152 (2021), 69-93.
- M. Domínguez-Vázquez, J. M. Manzano: Isoparametric surfaces in E(κ, τ)-spaces, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 22 (2021), 269-285.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, A. Kollross: On homogeneous manifolds whose isotropy actions are polar, Manuscripta Math. 161 (2020), 15-34.
- O. Pérez-Barral: Some problems on ruled real hypersurfaces in non flat complex space forms, Results Math., 75, 167 (2020).
- M. Domínguez-Vázquez, O. Pérez-Barral: Ruled hypersurfaces with constant mean curvature in complex space forms, J. Geom. Phys. 144 (2019), 121-125.
- A. Rodríguez-Vázquez: A nonisoparametric hypersurface with constant principal curvatures, Proc. Amer. Math. Soc. 147 (2019), 5417-5420.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, C. Vidal-Castiñeira: Strongly 2-Hopf hypersurfaces in complex projective and hyperbolic planes, Ann. Mat. Pura Appl. 197 (2018), 469-486.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, C. Vidal-Castiñeira: Isoparametric submanifolds in two-dimensional complex space forms, Ann. Global Anal. Geom. 53 (2018), 205-216.
- M. Domínguez-Vázquez, C. Gorodski: Polar foliations on quaternionic projective spaces, Tohoku Math. J. 70 (2018), 353-375.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, V. Sanmartín-López: Isoparametric hypersurfaces in complex hyperbolic spaces, Adv. Math. 314 (2017), 756-805.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, A. Kollross: Polar actions on complex hyperbolic spaces, Math. Z. 287 (2017), 1183-1213.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, C. Vidal-Castiñeira: Real hypersurfaces with two principal curvatures in complex projective and hyperbolic planes, J. Geom. Anal. 27 (2017), 442-465.
- J. Berndt, J. C. Díaz-Ramos, M. Vanaei: Cohomogeneity one actions on Minkowski spaces, Monatsh. Math. 184 (2017), 185-200.
- J. C. Díaz-Ramos, S. M. B. Kashani, M. Vanaei: Cohomogeneity one actions on anti de Sitter spacetimes, Results Math. 72 (2017), 515-536.
- V. Sanmartín-López: Spacelike isoparametric hypersurfaces, Differential Geom. Appl., 54, Part A (2017), 53-58.
- M. Domínguez-Vázquez: Isoparametric foliations on complex projective spaces, Trans. Amer. Math. Soc. 368 (2016), 1211-1249.
- J. C. Díaz-Ramos, C. Vidal-Castiñeira: Examples of real hypersurfaces with two principal curvatures in complex projective planes, Int. J. Geom. Meth. Mod. Physics 12 (2015), 1560013 (6 pages).
- M. Domínguez-Vázquez: Canonical extension of submanifolds and foliations in noncompact symmetric spaces, Int. Math. Res. Not. (IMRN) 22 (2015), 12114-12125.
- J. Berndt, M. Domínguez-Vázquez: Cohomogeneity one actions on some noncompact symmetric spaces of rank two, Transform. Groups 20 (2015), 921-938.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez: Isoparametric hypersurfaces in Damek-Ricci spaces, Adv. Math. 239 (2013), 1-17.
- J. Berndt, J. C. Díaz-Ramos: Polar actions on the complex hyperbolic plane, Ann. Global Anal. Geom. 43 (2013), 99-106.
- J. Berndt, J. C. Díaz-Ramos: Homogeneous polar foliations of complex hyperbolic spaces, Comm. Anal. Geom. 20 (2012), 435-454.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez: Inhomogeneous isoparametric hypersurfaces in complex hyperbolic spaces, Math. Z. 271 (2012), 1037-1042.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez: Non-Hopf real hypersurfaces with constant principal curvatures in complex space forms, Indiana Univ. Math. J. 60 (2011), 859-882.
- J. C. Díaz-Ramos, A. Kollross: Polar actions with a fixed point, Differential Geom. Appl. 29 (2011), 20-25.
- M. Domínguez-Vázquez: Real hypersurfaces with constant principal curvatures in complex space forms, Differential Geom. Appl., 29, suppl. 1, (2011), 65-70.
- J. Berndt, J. C. Díaz-Ramos, H. Tamaru: Hyperpolar homogeneous foliations on symmetric spaces of noncompact type, J. Differential Geom. 86 (2010), 191-235.
- J. Berndt, J. C. Díaz-Ramos: Homogeneous hypersurfaces in complex hyperbolic spaces, Geom. Dedicata 138 (2009), 129-150.
- J. Berndt, J. C. Díaz-Ramos: Real hypersurfaces with constant principal curvatures in the complex hyperbolic plane, Proc. Amer. Math. Soc. 135 (2007), 3349-3357.
- J. Berndt, J. C. Díaz-Ramos: Real hypersurfaces with constant principal curvatures in complex hyperbolic spaces, J. London Math. Soc. 74 (2006), 778-798.
Conference proceedings
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, V. Sanmartín-López: Submanifold geometry in symmetric spaces of noncompact type, Sao Paulo J. Math. Sci., (Special Section: An Homage to Manfredo P. do Carmo), 2021, 75-110.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, V. Sanmartín-López: Anti-De Sitter spacetimes and isoparametric hypersurfaces in complex hyperbolic spaces, Lorentzian Geometry and Related Topics, Springer Proceedings in Mathematics & Statistics 211, GeLoMa 2016, Málaga, Spain, September 20-23, Springer, 2017, 87-101.
- J. C. Díaz-Ramos: Polar Actions on Symmetric Spaces, Recent Trends in Lorentzian Geometry, Springer Proceedings in Mathematics & Statistics, Springer, 2013, 315-334.
- M. Domínguez-Vázquez: On the existence of inhomogeneous isoparametric foliations of higher codimension on complex projective spaces, Pure and Applied Differential Geometry - PADGE 2012 (In Memory of Franki Dillen), Shaker Verlag, 2013, 114-125.
- M. Domínguez-Vázquez: Some interesting families of non-Hopf real hypersurfaces in complex space forms, Proceedings of The Seventeenth International Workshop on Differential Geometry and related fields 17, 2013, 113-124.
- M. Domínguez-Vázquez: On isoparametric hypersurfaces in complex hyperbolic spaces, International Meeting on Differential Geometry (Córdoba 2010), Universidad de Córdoba, 2013, 71-92.
- J. C. Díaz-Ramos: Polar actions on complex space forms, Proceedings of The Sixteenth International Workshop on Differential Geometry and related fields 16, 2012, 69-88.
- M. Domínguez-Vázquez: On an inhomogeneous isoparametric family of hypersurfaces with constant principal curvatures in the Cayley hyperbolic plane, XX International Fall Workshop on Geometry and Physics, AIP Conference Proceedings 1460, Amer. Inst. Phys., 2012, 169-173.
- J. C. Díaz-Ramos: The orbits of cohomogeneity one actions on complex hyperbolic spaces, Proceedings of the VIII International Colloquium on Differential Geometry, World Sci. Publ. Co., 2009, 146-155.
Talks
This is a list of talks related to this research project. For a more complete list of my talks click here.
Conference talks
- J. C. Díaz-Ramos: Homogeneous Lagrangian foliations in complex spaces forms, Workshop on Manifolds with Symmetries, Stuttgart, Germany, -.
- M. Domínguez-Vázquez: Extension of submanifolds in symmetric spaces of noncompact type, Workshop on Manifolds with Symmetries, Stuttgart, Germany, -.
- V. Sanmartín-López: Codimension one Ricci solitons in Iwasawa groups, Workshop on Manifolds with Symmetries, Stuttgart, Germany, -.
- A. Rodríguez-Vázquez: Totally geodesic submanifolds in products of rank one symmetric spaces, Workshop on Manifolds with Symmetries, Stuttgart, Germany, -.
- T. Otero-Casal: Homogeneous hypersurfaces of symmetric spaces of noncompact type, Workshop on Manifolds with Symmetries, Stuttgart, Germany, -.
- J. M. Lorenzo-Naveiro: Polar actions on some noncompact symmetric spaces, Workshop on Manifolds with Symmetries, Stuttgart, Germany, -.
- J. C. Díaz-Ramos: Cohomogeneity one actions on rank one symmetric spaces of noncompact type, Geometry of symmetric spaces and group actions, online, Japan, -.
- M. Domínguez-Vázquez: Cohomogeneity one actions on symmetric spaces of noncompact type and higher rank, Geometry of symmetric spaces and group actions, online, Japan, -.
- A. Rodríguez-Vázquez: Totally geodesic submanifolds and Kähler angle in symmetric spaces, Symmetry and Shape, Santiago de Compostela, Spain, -.
- T. Otero-Casal: Cohomogeneity one actions on irreducible and reducible symmetric spaces of noncompact type, Symmetry and Shape, Santiago de Compostela, Spain, -.
- J. M. Lorenzo-Naveiro: Polar homogeneous foliations on SL(3,R)/SO(3), Symmetry and Shape, Santiago de Compostela, Spain, -.
- A. Rodríguez-Vázquez: Symmetric spaces: holonomy and totally geodesic submanifolds, PG Forum, Lancaster, United Kingdom, .
- O. Pérez-Barral: Subvariedades CR homogéneas en el espacio hiperbólico complejo, Congreso de Jóvenes Investigadores RSME, Castelló, Spain, -.
- A. Rodríguez-Vázquez: Isoparametricidad e isospectralidad del operador forma, Congreso de Jóvenes Investigadores RSME, Castelló, Spain, -.
- A. Rodríguez-Vázquez: Homogeneous and inhomogeneous isoparametric hypersurfaces in quaternionic hyperbolic spaces, Workshop on Geometric Analysis IEMATH-GR, Granada, Spain, .
- J. C. Díaz-Ramos: Homogeneous submanifolds in complex space forms, Symmetry and shape, Celebrating the 60th birthday of Prof. J. Berndt, Santiago de Compostela, Spain, -.
- O. Pérez-Barral: Homogeneous CR submanifolds in complex hyperbolic spaces, Symmetry and shape: Celebrating the 60th birthday of Prof. J. Berndt, Santiago de Compostela, Spain, -.
- M. Domínguez-Vázquez: Cohomogeneity one isometric actions on quaternionic hyperbolic spaces, Encuentro de Topología 2019, Santiago de Compostela, Spain, -.
- A. Rodríguez-Vázquez: A non isoparametric hypersurface with constant principal curvatures, Differential Geometry and its Applications, Hradrec Králové, Czech Republic, -.
- M. Domínguez-Vázquez: Homogeneous and inhomogeneous isoparametric hypersurfaces in symmetric spaces of noncompact type, Workshop on the Isoparametric Theory, Beijing , China, -.
- M. Domínguez-Vázquez: Isoparametric surfaces in E(κ, τ)-spaces, Encuentro de la Red Española de Análisis Geométrico, Murcia, Spain, .
- J. C. Díaz-Ramos: Cohomogeneity one actions on Minkowski spaces, II joint meeting Brazil-Spain in Mathematics, Cádiz, Spain, -.
- M. Domínguez-Vázquez: Nonlinear overdetermined boundary problems in Riemannian manifolds, II joint meeting Brazil-Spain in Mathematics, Cádiz, Spain, -.
- M. Domínguez-Vázquez: Subvariedades e accións isométricas en espazos simétricos de tipo non compacto, Seminario Vidal Abascal, Santiago de Compostela, Spain, -.
- M. Domínguez-Vázquez: Isoparametric surfaces in homogeneous 3-spaces, Preliminary talks of the ICM Satellite Conference Modern Trends in Differential Geometry, São Paulo, Brazil, .
- M. Domínguez-Vázquez: Cohomogeneity one actions on symmetric spaces of noncompact type, Seminar, Rio de Janeiro, Brazil, .
- O. Pérez-Barral: Ruled hypersurfaces with constant mean curvature in complex space forms are minimal, First BYMAT Conference: Bringing Young Mathematicians Together, Madrid, Spain, -.
- V. Sanmartín-López: Isospectral submanifolds in non-compact symmetric spaces, Hiroshima Differential Geometry Day 2018, Hiroshima, Japan, .
- V. Sanmartín-López: Homogeneous and isoparametric hypersurfaces in complex hyperbolic spaces, Geometry of Submanifolds and Integrable Systems, Osaka, Japan, -.
- M. Domínguez-Vázquez: Isoparametric hypersurfaces in the complex hyperbolic space, Primer Encuentro Conjunto RSME-UMA, Buenos Aires, Argentina, -.
- J. C. Díaz-Ramos: Homogeneous submanifolds of complex space forms, The third Japanese-Spanish workshop on Differential Geometry, Madrid, Spain, -.
- M. Domínguez-Vázquez: Isoparametric hypersurfaces in complex hyperbolic spaces, IV Encuentro Conjunto RSME-SMM, Valladolid, Spain, -.
- V. Sanmartín-López: Description and classification of isoparametric submanifolds in the complex hyperbolic space, Differential Geometry, Bedlewo, Poland, -.
- M. Domínguez-Vázquez: Submanifolds and isometricactions on symmetric spaces of noncompact type, Seminar, São Paulo, Brazil, - .
- J. C. Díaz-Ramos: Cohomogeneity one actions on Minkowski spaces, 8th International Meeting on Lorentzian Geometry, Málaga, Spain, -.
- M. Domínguez-Vázquez: Isoparametric submanifolds of complex space forms, XXV International Fall Workshop on Geometry and Physics, Madrid, Spain, - .
- V. Sanmartín-López: Anti-De Sitter and complex hyperbolic spaces: their isoparametric hypersurfaces, Differential Geometry and its Applications, Brno, Czech Republic, -.
- J. C. Díaz-Ramos: Isoparametric hypersurfaces in complex hyperbolic spaces, Second joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies, Logroño, Spain, -.
- J. C. Díaz-Ramos: Non-proper cohomogeneity one actions on Minkowski spaces, First joint meeting Brazil-Spain in Mathematics, Fortaleza, Brazil, -.
- M. Domínguez-Vázquez: Classification of isoparametric hypersurfaces in complex hyperbolic spaces, First joint meeting Brazil-Spain in Mathematics, Fortaleza, Brazil, -.
- C. Vidal-Castiñeira: Hipersuperficies de cohomogeneidad uno en los planos proyectivo e hiperbólico complejos, Congreso de Jóvenes Investigadores, Murcia, Spain, -.
- V. Sanmartín-López: Clasificación de hipersuperficies isoparamétricas en el espacio hiperbólico complejo, Congreso de Jóvenes Investigadores, Murcia, Spain, -.
- C. Vidal-Castiñeira: Cohomegeneity one hypersurfaces in the complex projective and hyperbolic planes, XXIV International Fall Workshop on Geometry and Physics, Zaragoza, Spain, -.
- V. Sanmartín-López: Hipersuperficies isoparamétricas en el espacio hiperbólico complejo, XI Encuentro Andaluz de Geometría, Sevilla, Spain, .
- J. C. Díaz-Ramos: Polar actions on symmetric spaces, RSME Conference 2015, Granada, Spain, -.
- M. Domínguez-Vázquez: Two construction methods of isoparametric hypersurfaces in noncompact symmetric spaces, RSME Conference 2015, Granada, Spain, -.
- C. Vidal-Castiñeira: Hipersuperficies con dos curvaturas principales en CP^2 y CH^2, RSME Conference 2015, Granada, Spain, -.
- M. Domínguez-Vázquez: Classification of isoparametric foliations on complex projective spaces, Geometry and Dynamics of Foliations, Madrid, Spain, - .
- M. Domínguez-Vázquez: Polar actions on complex hyperbolic spaces II, XVIII Escola de Geometria Diferencial, Brasilia, Brazil, - .
- J. C. Díaz-Ramos: Real hypersurfaces in complex space forms, The second Japanese-Spanish workshop on Differential Geometry, Tokyo, Japan, -.
- M. Domínguez-Vázquez: Isoparametric submanifolds of complex projective spaces, The second Japanese-Spanish workshop on Differential Geometry, Tokyo, Japan, -.
- M. Domínguez-Vázquez: Some interesting families of non-Hopf real hypersurfaces in complex space forms, 17th International Workshop on Differential Geometry, Daejeon, South Korea, - .
- M. Domínguez-Vázquez: Familias isoparamétricas en espacios de Damek-Ricci, Congreso de Jóvenes Investigadores de la RSME, Seville, Spain, -.
- M. Domínguez-Vázquez: The horospherical decomposition and new isoparametric hypersurfaces in noncompact symmetric spaces, Geometric Analysis Seminar GAS-UV13, Valencia, Spain, -.
- J. C. Díaz-Ramos: Polar actions on complex space forms II, The 16th International Workshop on Differential Geometry & Related Topics, Daegu, South Korea, -.
- J. C. Díaz-Ramos: Polar actions on complex space forms I, Pre-joint Meeting of The 16th International Workshop on Differential Geometry, Daegu, South Korea, .
- M. Domínguez-Vázquez: Polar foliations for beginners, Geometry Meeting 2012, Ferrol, Spain, .
- M. Domínguez-Vázquez: On the existence of inhomogeneous isoparametric foliations of higher codimension on complex projective spaces, Conference on Pure and Applied Differential Geometry PADGE 2012, Leuven, Belgium, -.
- J. C. Díaz-Ramos: Polar actions on complex hyperbolic spaces, Differential Geometry Days, Santiago de Compostela, Spain, -.
- M. Domínguez-Vázquez: Isoparametric foliations on complex projective spaces, Differential Geometry Days, Santiago de Compostela, Spain, -.
- J. C. Díaz-Ramos: Polar actions on noncompact symmetric spaces, 2nd European Young and Mobile Workshop, Geometric Analysis and Partial Differential Equations, Granada, Spain, -.
- J. C. Díaz-Ramos: Polar actions on symmetric spaces of noncompact type, VI International Meeting on Lorentzian Geometry, Granada, Spain, -.
- M. Domínguez-Vázquez: Families of parallel CMC hypersurfaces in noncompact rank-one symmetric spaces, VI International Meeting on Lorentzian Geometry, Granada, Spain, -.
- M. Domínguez-Vázquez: Principal curvatures of isoparametric hypersurfaces in complex hyperbolic spaces, Conference in Geometry and Global Analysis, Santiago de Compostela, Spain, -.
- M. Domínguez-Vázquez: On isoparametric hypersurfaces in complex hyperbolic spaces, International Meeting on Differential Geometry, Córdoba, Spain, -.
- M. Domínguez-Vázquez: O problema da clasificación das hipersuperficies isoparamétricas, Encontro de Xeometría 2010, Ferrol, Spain, .
- M. Domínguez-Vázquez: Real hypersurfaces with constant principal curvatures in complex space forms, DGA 2010 - Differential Geometry and its Applications, Brno, Czech Republic, -.
- J. C. Díaz-Ramos: Homogeneous hyperpolar foliations on symmetric spaces of noncompact type, Workshop on Hypersurface Geometry and Integrable Systems, Sendai, Japan, -.
- M. Domínguez-Vázquez: Real hypersurfaces with constant principal curvatures in complex projective and hyperbolic spaces, Workshop on Hypersurface Geometry and Integrable Systems, Sendai, Japan, -.
- J. C. Díaz-Ramos: Acciones hiperpolares en espacios simétricos no compactos, Geometry Meeting 2009, Ferrol, Spain, -.
- J. C. Díaz-Ramos: Hyperpolar actions on noncompact symmetric spaces, II Congreso latinoamericano de grupos de Lie en geometría, La Falda, Argentina, -.
- J. C. Díaz-Ramos: Hypersurfaces with constant principal curvatures in the complex hyperbolic space, VIII International Colloquium on Differential Geometry, Santiago de Compostela, Spain, -.
- J. C. Díaz-Ramos: A characterisation of real hypersurfaces with constant principal curvatures, Differential Geometry, Bedlewo, Poland, -.
- J. C. Díaz-Ramos: Homogeneous hypersurfaces in the complex hyperbolic space, Irish Geometry Conference, Galway, Ireland, -.
Invited seminar talks
- J. C. Díaz-Ramos: Cohomogeneity one actions on quaternionic hyperbolic spaces, Symmetric spaces seminar, online, United Kingdom, .
- M. Domínguez-Vázquez: Cohomogeneity one actions and inhomogeneous isoparametric hypersurfaces in quaternionic hyperbolic spaces, Differential Geometry Seminar, online, Germany, .
- A. Rodríguez-Vázquez: Homogeneous and inhomogeneous isoparametric hypersurfaces in symmetric spaces, Junior Geometry Seminar KCL/UCL, London, United Kingdom, .
- M. Domínguez-Vázquez: On isoparametric hypersurfaces in noncompact symmetric spaces, Seminar, Norman, United States, .
- M. Domínguez-Vázquez: Overdetermined elliptic problems in Riemannian manifolds, Seminar, South Bend, United States, .
- M. Domínguez-Vázquez: Isoparametric surfaces in homogeneous 3-manifolds, Seminar, St. Louis, United States, .
- M. Domínguez-Vázquez: Polar foliations on symmetric spaces, Colloquium, St. Louis, United States, .
- M. Domínguez-Vázquez: Isoparametric surfaces in homogeneous spaces, Seminario Vidal Abascal, Santiago de Compostela, Spain, .
- V. Sanmartín-López: Description of isoparametric hypersurfaces in the complex hyperbolic space, Seminario de Geometría, Madrid, Spain, .
- V. Sanmartín-López: On the classification of isoparametric hypersurfaces, Geometry Seminar, Cologne, Germany, .
- J. C. Díaz-Ramos: Isoparametric hypersurfaces in complex space forms, Department of Mathematics Seminar, Stuttgart, Germany, .
- V. Sanmartín-López: Isoparametric hypersurfaces in the anti-De Sitter space and the complex hyperbolic space, Geometry Seminar, London, United Kingdom, .
- M. Domínguez-Vázquez: Isoparametric hypersurfaces in overdetermined PDE problems, Seminario Vidal Abascal, Santiago de Compostela, Spain, .
- M. Domínguez-Vázquez: Clasificación das foliacións polares no espazo proxectivo cuaterniónico, Seminario Vidal Abascal, Santiago de Compostela, Spain, .
- J. C. Díaz-Ramos: On the classification of polar actions on complex hyperbolic spaces, Workshop on submanifolds in complex space forms, London, United Kingdom, .
- C. Vidal-Castiñeira: Strongly 2-Hopf hypersurfaces in complex projective and hyperbolic planes, Workshop on submanifolds in complex space forms, London, United Kingdom, .
- V. Sanmartín-López: On the classification of isoparametric hypersurfaces in complex hyperbolic spaces, Workshop on submanifolds in complex space forms, London, United Kingdom, .
- M. Domínguez-Vázquez: Polar foliations on quaternionic projective spaces, Geometry Seminar, São Paulo, Brazil, .
- V. Sanmartín-López: Isoparametric families of hypersurfaces in complex hyperbolic spaces, Differential Geometry Seminar, Rio de Janeiro, Brazil, .
- J. C. Díaz-Ramos: Cohomogeneity one actions on the Minkowski space, Seminar, Rio de Janeiro, Brazil, .
- J. C. Díaz-Ramos: Foliaciones polares e isoparamétricas, Department of Mathematics Seminar, Bilbao, Spain, .
- M. Domínguez-Vázquez: Polar foliations on complex projective space, Seminar, Rio de Janeiro, Brazil, .
- M. Domínguez-Vázquez: Introduction to isoparametric foliations, Seminar, Sao Paulo, Brazil, -.
- M. Domínguez-Vázquez: Inhomogeneous isoparametric foliations and prime numbers, Seminar, Sao Paulo, Brazil, .
- M. Domínguez-Vázquez: Homogeneity of isoparametric submanifolds and prime numbers, Seminar, Brasilia, Brazil, .
- M. Domínguez-Vázquez: Hypersurfaces with two principal curvatures in nonflat complex space forms, Department of Mathematics Seminar, IMPA, Rio de Janeiro, Brazil, .
- M. Domínguez-Vázquez: A geometric characterization via prime numbers, Department of Mathematics Seminar, Universidade Federal Fluminense, Rio de Janeiro, Brazil, .
- M. Domínguez-Vázquez: Inhomogeneous isoparametric foliations, Department of Mathematics Seminar, London, United Kingdom, .
- M. Domínguez-Vázquez: The classification problem of isoparametric foliations, ICMAT Seminar, Madrid, Spain, .
- M. Domínguez-Vázquez: Inhomogeneous isoparametric families on complex projective spaces, Department of Mathematics Seminar, Stuttgart, Germany, .
- J. C. Díaz-Ramos: A classification of polar actions on complex hyperbolic spaces, Department of Mathematics Seminar, Cologne, Germany, .
- J. C. Díaz-Ramos: Isoparametric hypersurfaces in complex space forms, Department of Mathematics Seminar, Darmstadt, Germany, .
- J. C. Díaz-Ramos: Foliaciones polares homogéneas en espacios hiperbólicos complejos, Xornada de Xeometría (Seminario Vidal Abascal), Santiago de Compostela, Spain, .
- M. Domínguez-Vázquez: Homogeneous and isoparametric hypersurfaces in non-compact rank-one symmetric spaces, Department of Mathematics Seminar, Cologne, Germany, .
- J. C. Díaz-Ramos: Non-Hopf real hypersurfaces with constant principal curvatures in complex space forms, Department of Mathematics Seminar, Cologne, Germany, .
- J. C. Díaz-Ramos: Homogeneous hyperpolar foliations on symmetric spaces of noncompact type, Department of Mathematics Seminar, Cologne, Germany, .
- J. C. Díaz-Ramos: Hyperpolar homogeneous foliations on noncompact symmetric spaces, Department of Mathematics Seminar, Augsburg, Germany, .
- J. C. Díaz-Ramos: Hypersurfaces with constant principal curvatures in the complex hyperbolic space, Hiroshima University Topology-Geometry Seminar, Hiroshima, Japan, .
- J. C. Díaz-Ramos: Hipersuperficies homoxéneas no espazo hiperbólico real, Seminario de Xeometría e Topoloxía, Santiago de Compostela, Spain, .
Posters
- A. Rodríguez-Vázquez: Non-Hopf hypersurfaces with constant principal curvatures in complex projective space and complex hyperbolic space, Congreso Bienal de la RSME, Santander, Spain, -.
- O. Pérez-Barral: Ruled hypersurfaces with constant mean curvature in complex space forms, XXV Encuentro de Topología, Barcelona, Spain, -.
- A. Rodríguez-Vázquez: Hypersurfaces with constant principal curvatures in complex hyperbolic spaces, XXV Encuentro de Topología, Barcelona, Spain, -.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, C. Vidal-Castiñeira: Real hypersurfaces with two constant principal curvatures in complex projective and hyperbolic planes, XXIII International Fall Workshop on Geometry and Physics, Granada, Spain, -.
- M. Domínguez-Vázquez: Some results on isoparametric hypersurfaces in nonflat complex space forms, XX International Fall Workshop on Geometry and Physics, Madrid, Spain, - .
- J. C. Díaz-Ramos, M. Domínguez-Vázquez: Principal curvatures of isoparametric hypersurfaces in complex hyperbolic spaces II, Conference in Geometry and Global Analysis, Santiago de Compostela, Spain, -.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez: Hypersurfaces with constant principal curvatures in complex projective and hyperbolic spaces, Lectures on Lorentzian Geometry, Granada, Spain, -.