Santiago de Compostela, 7-11 July 2008

Brief portrait of the life and work of Prof. Enrique Vidal Abascal

Enrique Vidal Abascal was born in Oviedo in October 12, 1908, and died in Santiago de Compostela in October 31, 1994. Son of a galician whose job was the one of Delegate of the Ministry of Finances, the successive transfers of his father take him to reside, from the two years of age, in Ourense, A Coruña, and finally in Santiago de Compostela. His life was centered, therefore, in Galicia, of which he always felt a son in spite of have been born, by familiar circumstances, outside of it.

He studies the baccalaureate in the Institutes of A Coruña and Santiago de Compostela. (At this level, an Institute is the equivalent, in Spain, to a Licée in France or to a College in USA). His taste and vocation towards mathematics take him to make his studies of degree in Exact Sciences, reason why he was forced to go to Madrid, since at that time these studies only existed in the Universities of Madrid, Barcelona and Zaragoza.

His paternal family had a house in Lalín (Pontevedra), where he spent his vacations of summer, fact that caused that Vidal Abascal entered in contact, from a very early age, with the insigne priest and astronomer D. Ramón Maria Aller Ulloa, friend of the family and, in particular, of his father.

Some significant data of the “Curricullum Vitae” of Prof. Vidal Abascal are the following ones:

- Graduated in Exact Sciences by the University Complutense of Madrid (1931), he immediately happens to obtain a nomination as Assistant Professor of Analytical Geometry, by public competitive examination, position in which stays for only a few months, because he got the position, in April of 1933, of Professor of Mathematics of Institute, being his first post at the Institute of Santa Cruz de La Palma (Canary Islands). He only remains few months in this post, because he is nominated as Director, in the course 1933-34, of the just created Institute of Monforte de Lemos (Lugo). Between the years 1933 to 1955, Prof. Vidal Abascal goes successively as Professor through the Institutes of Monforte de Lemos (Lugo), La Estrada (Pontevedra), courses 1935-36 and 36-37, Vigo, course 1937-38 and 38-39, Pontevedra, courses 1939-40 and 40-41, and Santiago de Compostela, from the course 1941-42, where he shares his Chair with a post of Assistant Professor in the Faculty of Sciences of the University of Santiago de Compostela.
- In 1944 he obtained the Title of Doctor in Exact Sciences by the University Complutense of Madrid; his Doctoral Thesis was made under the guidance of D. Ramon Maria Aller Ulloa, being his advisor Prof. Esteban Terradas (University Complutense), and was about the geometric study of the calculation of double star orbits.
- In 1955 he obtained, by public competitive examination, the Chair of Differential Geometry of the University of Santiago de Compostela, Chair where he stayed during 23 years, until the moment of his retirement, in October of 1978.
- During his university academic life he carried out the following positions:
- Vicedean of the Faculty of Sciences of the University of Santiago de Compostela during the periods 1960-61, 1966-69 and 1976-78.
- Dean of the Faculty of Mathematics of the University of Santiago de Compostela from January to October of 1978, date of his retirement.
- Vicepresident of the Royal Spanish Mathematical Society in the periods 1963-66 and 1973-78.
- Head of the Mathematical Section of the Astronomical Observatory of the University of Santiago de Compostela, associate to the “Consejo Superior de Investigaciones Científicas” (Spain), from 1942.
- Director of the Seminary of Mathematics of the University of Santiago de Compostela, center coordinated with the Institute “Jorge Juan” of the “Consejo Superior de Investigaciones Científicas”, between 1967 and 1978.

Vidal Abascal was Member of the Royal Academy of Galicia from 1971, occupying in this Institution the vacancy produced by the death of D. Ramon Maria Aller Ulloa.

The creation of the Royal Academy of Sciences of Galicia, carried out in 1978, is owed to his personal initiative and managements. He was the first president of this Academy between 1978 and 1982, when he resigned and is nominated as Honorary President.

Member of the “American Mathematical Society”, of the “Círcolo Matemático di Palermo” and of the Royal Spanish Mathematical Society, he was also reviewer of “Mathematical Reviews” (USA) and of “Zentralblatt für Mathematik” (Germany).

In 1952 he visited the “Bureau International d' Education” in Geneva (Switzerland), with a grant of the “Junta de Ampliación de Estudios”, visiting training centers in Switzerland to know the problematic of the teaching of Mathematics at the Secondary Level in this country; in 1953 he traveled again to Switzerland, with a grant of the “Consejo Superior de Investigaciones Científicas”, staying three months in Lausanne, working with Prof. Georges de Rham on the foundations of Integral Geometry, and being invited to pronounce a conference in the Polytechnical School of this city.

In 1963, 1966, 1973 and 1977 he was invited to pronounce conferences and to lecture courses on the subjects of his investigations in the University of Paris VI. Also he was invited to participate in numerous seminaries and scientific meetings in the Universities of Paris and Strasbourg, and in the research centers of Oberwolfach and Brussels. He also participated in the International Congresses of Mathematicians celebrated in Edimburg (1958), Moscow (1966) and Nize (1970), in numerous “Annual Meetings of Spanish Mathematicians”, and in 1977 he was one of the invited lecturers in the “Reunión de Matemáticos de Expresión Latina” held in Palma de Mallorca.

The scientific interests of the Prof. Vidal Abascal were centered in three great areas:

- Astronomy, and in particular in the calculation of double star orbits.
- Classic Differential Geometry (curves and surfaces) and Integral Geometry.
- Differential Geometry of Manifolds, and in this context in particular in the Theory of Foliations, Almost-Product Structures and Hermitian Geometries.

An objective proof of the interest and importance of the investigations made by Prof. Vidal Abascal is the fact that many of their articles were published in important world-wide distributed journals of recognized prestige; among them:

- Astronomical Journal (Yale, USA)
- Journal of Differential Geometry (Leigh Univ., USA)
- Proceedings of the American Mathematical Society (USA)
- Bulletin of the American Mathematical Society (USA)
- Annals de l’Institut Fourier (Grenoble, France)
- Comptes Rendu de l’Académie des Sciences (París, France)
- Rendiconti dei Círcolo Matemático di Palermo (Palermo, Italy)
- Tensor N.S. (Japan)

He was a very prolific author, and in the list of his publications, probably incomplete, included at the end of this “Brief Portrait”, there are a total of 87 publications that can be grouped in the following form: 3 monographs and 13 articles on Astronomy; 1 book, 5 monographs and 39 articles on Differential and Integral Geometry, and 26 publications more: books on general Mathematics, discourses, books of essay, and articles of divulgation in prestigious magazines, like for example in “Revista de Occidente” (Spain).

Vidal Abascal received, during his life, several prizes by his scientific work:

**“Prize Alfonso X El Sabio”**, of the “Consejo Superior de Investigaciones Científicas”, in 1949, by his work “Geometría Integral sobre las Superficies Curvas”.**“Prize of the Royal Academy of Exact, Physical and Natural Sciences” (Spain)**, in two occasions: in 1953 by his work “Generalización de los Invariantes Integrales”; in 1959 by his work “Equivalencia entre algunos problemas del Cálculo de Variaciones, la Teoría de los Invariantes Integrales Generalizados y la Geometría Integral”.**“Prize of Research of the Xunta of Galicia” (Galicia, Spain)**, in 1989, prize that was granted to him by the whole of his scientific work.

He also received the following medals:

**“Officier dans l' Ordre des Palmes Académiques”**, granted by the French Government, in 1974.**“Medalla Castelao”**, granted by the Xunta of Galicia in 1986, recognition of a whole life dedicated to Galicia.

It is certainly impossible to summarize, in this brief portrait, which have been the most significant results obtained by Prof. Vidal Abascal throughout his wide life as researcher. Nevertheless, if the work of a man dedicated to the scientific research not only must be valued by the quality of his results, but also by the echo that these results have had in the investigations of other students of such subjects, it is not difficult to state the high level of the mathematical research done by Vidal Abascal.

An important and significant part of the whole of his research was published as articles in prestigious journals of world-wide scope and diffusion, journals in which the articles are only published if, in the opinion of prestigious specialists which act as “referees”, they are worth of being published by their quality and interest. In spite of this, it could happen that a certain study happened unnoticed because it does not fit in most popular lines of research at a determined moment, reason why it is essential to valuate its influence in the studies and researches of other mathematicians. In the case of Prof. Vidal Abascal such a valuation unavoidably must be very positive; his articles have been mentioned very frequently by other authors and, in fact, some of among those articles are still included as a reference in the specialized monographs in spite of the time passed from their publication.

The interest of Vidal Abascal in his studies of Astronomy was mainly centered in the calculation of double star orbits, subject of his doctoral thesis. When commenting his works on this subject, Prof. Baize, of the Astronomical Observatory of Paris (France), one of the maximum authorities of the world on this topic at that time, wrote in 1979 the following:

“Prof. Vidal is first of all a mathematician, his works on Differential Geometry universally well-known and appreciated are an evidence of that. He has not observed personally double stars, but he has been interested in the problems that arise in the calculation of its orbits, calculation for which there exist numerous methods, of an unequal practical value, and that can be classified in two groups; graphical methods and analytical methods. The method imagined by Vidal belongs to the second group, but it solves the problem by completely new routes, giving an elegant proof and applying it to the star calculations… The whole of his research, as much on the nonelliptical orbits as on the elliptical ones, has been condensed by Vidal in a very important work, published in 1953, entitled “Calculation of Apparent Orbits of Double Stars”, book that constitutes without a doubt, as I already wrote in the moment of its appearance, the most remarkable contribution in our time to the study of the double star orbits. On the other hand, Vidal did not limit himself only to the theory, he was also interested in the practical application of his methods, inventing and making construct by the prestigious Swiss company Coradi his ingenious “Orbígrafo”, apparatus that allows to directly draw up on the paper the curve that represents the angles of position as a function of the distances, respecting rigorously the law of the areas. This instrument is still used by numerous researchers, mainly in the Astronomical Observatory of the University of Santiago.”

These appreciations of Prof. Baize on the importance of the contributions of Vidal Abascal in Astronomy are sufficiently clear and explanatory, reason why any other commentary seems unnecessary.

The first works of Vidal Abascal on Differential Geometry date from the years 1943-47. His studies on parallel curves on surfaces of constant curvature are specially outstanding, because they lead to a generalization of the classical formulas of Steiner for parallel connected curves in the plane; the methods used by Vidal in this study were used later by the prestigious geometrician C.B. Allendoerfer on the spheres. His works on these subjects, that belong to what at that time was known as Differential Geometry “in the large” (“in grossen”), take him in a natural way to consider the study of some problems of Integral Geometry on surfaces. His numerous contributions in this area have not been out of phase with the passage of time, and it is not difficult to find references to them in recent articles dedicated, for example, to the study of the volume of geodesic tubes in Riemann manifolds of arbitrary curvature.

The study of the integral invariants of geodesics leads Vidal to consider its generalization and, in the last term, to the study of the measures in foliated manifolds, via by which Vidal introduces himself in a new subject of research, very novel at that time, subject of which has been pioneering and introductory in Spain. Once again, the results obtained by Vidal Abascal between 1964 and 1967 continue being mentioned in recent publications on the topic.

From 1966, year in which the first doctoral thesis directed by him appears, Vidal stops being a solitary researcher and begins to form a compact team of researches constituted by young people graduated in the Section of Mathematics of the Faculty of Sciences of the University of Santiago de Compostela. The numerous subjects of thesis that Vidal proposes to his students extend his personal interests in research to other subjects, such as almost-product or almost-hermitian structures.

Between years 1966 and 1978 Prof. Vidal Abascal directed a total of fifteen doctoral theses and, to an age in which a certain diminution in his research activity would be logical, he published five articles on Differential Geometry, made four communications in Congresses and wrote three monographs. In his articles of these last years are again very remarkable contributions, such as the notion of almost foliated metric for almost-product structures, or the definition of two new types of almost-hermitian structures, whose scientific name universally accepted and adopted is the one of “geometries G1 and G2”, being the “G” by the adjective “Gallegas” as it was indicated specifically in the note published in the “Comptes Rendus” of the Academy of Sciences of Paris in which they appeared in 1976.

When E. Vidal Abascal arrives at the University, first as student and years later as professor, mathematics in Spanish was totally out of phase and almost isolated with respect to the currents of study followed in the most important research centers outside our borders. The first trips that he makes abroad allow him to state this reality, and he then becomes aware of the urgent and inexcusable necessity to put remedy to this situation. Vidal Abascal did not content himself, like many of his contemporary did, with speaking or writing about what it was precise to make to remedy this situation, instead of that he acted and organized.

Once his academic situation becomes steady when wining the Chair of Differential Geometry in Santiago de Compostela, and in spite of the enormous difficulties and obstacles that existed in that time for it, Vidal manages the first visits of prestigious foreign mathematicians to Santiago de Compostela. Between years 1959 and 1978 more than forty foreign professors visit Santiago, coming from Germany, Belgium, Brazil, France, England, Israel, Portugal, Rumania, Switzerland and U.S.A., and they lecture specialization courses, give conferences, or participate in the International Colloquia of which we will talk about later; among them the names of some of the most prestigious geometricians of those decades can be found, and it is a specially remarkable circumstance the fact that the Prof. René Deheuvels, from the University of Paris VII (France), was nominated as Visiting Professor of the University of Santiago de Compostela to lecture, during two consecutive courses, Courses of Doctorate with total academic validity, a singular case in the Spanish mathematics of that time.

These efforts and initiatives of Vidal Abascal were not recognized at Spanish level, as it had been of justice. Nevertheless, the French Government compensated his efforts granting to him the medal of “Officier dans l' Ordre des Palmes Académiques” in 1974. This medal was, at that time, rarely granted outside France, and with it the exceptional personality of the Prof. Vidal Abascal was recognized; Prof. Deheuvels in the act of imposition of this medal said:

“…(Vidal Abascal) he knew how to stimulate in fifteen years the mathematical activity in the Spanish Universities… He got, in few years, to make Santiago well known in the scientific world, not only by the outstanding Colloquia that he organized but also by his own scientific works or by the works of his students… the concession by the French Government of this medal shows that his reputation has exceeded widely the frontiers.”

Abounding in these words of Prof. Deheuvels, we must emphasize very specially the three International Colloquia on Differential Geometry celebrated in the University of Santiago de Compostela in 1963, 1967 and 1972, personally organized by Prof. Vidal Abascal, of which the first of them was, in fact, the first international congress of mathematics celebrated in Spain. In 1978 a fourth International Colloquium specially dedicated to Vidal was held as a tribute in the occasion of his academic retirement. Later three new Colloquia, celebrated in Santiago de Compostela in 1984, 1988 and 1994, gave a continuity to the series initiated under the direction of the Prof. Vidal Abascal.

Prof. Luis A. Santaló, of the University of Buenos Aires (Argentine), when commenting the set of the work of Vidal Abascal, wrote:

“It is fundamental to remark that the importance of his works is even, if not surpassed, by the fact of having created in Santiago de Compostela a School of Geometry from where some brilliant students have already went to another Spanish universities and there they are having an outstanding behaviour. He knew the way to form a School. He knew how to create and to direct, for long years, a center with its own publications, a place for important national and international congresses and meetings, obliged visit for the most outstanding figures of the time, who came there to lecture courses and conferences with the certainty that their teachings will felt in a land that has been diligently prepared by Vidal Abascal, who knew made of his Institute a warm and welcoming complement for the own beauties of Santiago. His work has been persistent and always directed with tenacity, intelligence and love. Students and colleagues know well of his extraordinary charming, the smoothness in his behaviour, the nobility in his relationship, and his cleverness in the direction.”

Hardly the meaning of the work of the Prof. Vidal Abascal could be expressed better than through the list of his direct students, list in which his teaching is concretely shown:

- Prof. Francisco Javier Echarte Reula, Catedrático de Geometría y Topología, Universidad de Sevilla (retired ).
- Prof. Antonio Martínez Naveira, Catedrático de Geometría y Topología, Universidad de Valencia.
- Prof. Luís Angel Cordero Rego, Catedrático de Geometría y Topología, Universidad de Santiago de Compostela.
- Prof. Xosé Masa Vázquez, Catedrático de Geometría y Topología, Universidad de Santiago de Compostela.
- Prof. María Luisa Fernández Rodríguez, Catedrática de Geometría y Topología, Universidad del País Vasco.
- Prof. Luís María Hervella Torrón, Catedrático de Geometría y Topología, Universidad de Santiago de Compostela.
- Prof. José Antonio Oubiña Galiñanes, Catedrático de Geometría y Topología, Universidad de Santiago de Compostela.
- Prof. María Angeles de Prada Vicente, Catedrática de Geometría y Topología, Universidad del País Vasco.
- Prof. Manuel de León Rodríguez, Profesor de Investigación, Consejo Superior de Investigaciones Científicas.
- Prof. Regina Castro Bolaño, Profesora Titular de Geometría y Topología, Universidad de Santiago de Compostela.
- Prof. Agustín Bonome Dopico, Profesor Titular de Geometría y Topología, Universidad de Santiago de Compostela.
- Prof. Concha Fuertes Fraile, Profesora Titular de Álgebra, Universidad Complutense (Madrid).
- Prof. Enrique Vidal Costa, Catedrático de Matemáticas, Escuela Universitaria de Formación del Profesorado, Universidad de Vigo.
- Prof. Pedro Martínez Gadea, Profesor Colaborador, Consejo Superior de Investigaciones Científicas.

As much in his address entrance speech as Member of the Royal Academy of Galicia (“The Crisis of the European University”, A Coruña, 1971), like in his essay “Science and the Socialized University” (Ed. Dossat, Madrid 1972), or in his numerous journalistic collaborations, Vidal Abascal showed clearly his restlessness before the crisis by which the Spanish university in general was passing through, and in particular the crisis of the galician university, that at that time was reduced to the University of Santiago de Compostela. Through his writings his will of liberal and progressive man is clear, deeply worried about an university unable to give a suitable answer to the social demands of its time.

In all his writings, Vidal Abascal repeatedly denounced the marginalization that underwent Galicia from the Central Administration of the State in the university level; his comparative references with respect to other regions of Spain, in which already numerous new universities had been created, were continuous in those times, whereas in Galicia they continued to maintain an only university, a fact which produced an increasing imbalance between the total population of Galicia and the number of existing university positions. Also in the Vidal Abascal writings the poverty of the resources destined to promote the research, as much basic as applied, were object of reflection as well as the necessity of making a suitable and long-term planning that allowed to obtain a greater profitability of the limited existing resources, or the deficiencies in the system of access to the university or in the systems of formation and promotion of its teaching staff.

The taste of Vidal Abascal for the painting come from his youth; in his time of professor at Institute in A Estrada (Pontevedra) he already makes a picture of the staff of professors, and another one of who later would be his wife, Dª Mª Teresa Costa. Since then Vidal continued painting with assiduity, although he confessed that the painting always had been for him only a “hobby”.

He made a first showing of his paintings in A Coruña, 1947; this was followed by some others in Santiago de Compostela (1948, 1975 and 1978), Vigo (1950 and 1976), Pontevedra (1974, 1975 and 1980), Ourense (1977), Madrid (1979) and Barcelona (1983).

Vidal Abascal also published diverse articles about painting and critic of art; in 1972 he pronounced a conference in the Galician Center of Buenos Aires (Argentine) about “The Galician Painting School”, and in 1979 he published a book titled “On the University and the Galician Painting” (Univ. of Santiago de Compostela, 1979). Many of his pictorial works appear at the present in museums and particular collections.