On the index of Symmetric Spaces

Jurgen Berndt - Londres

Xoves 15 de maio de 2014 ás 16:00 horas na aula 10

The classification of totally geodesic submanifolds in irreducible Riemannian symmetric spaces is still an open problem for rank greater than 2. Onishchik defined in 1980 the index of a symmetric space as the minimum of the codimensions of the totally geodesic submanifolds of the space. A classical result states that index 1 corresponds to spaces of constant curvature. Onishchik determined the symmetric spaces with index 2 and calculated the index of a few other symmetric spaces. Recently, in join work with Carlos Olmos, we made a new approach to this problem. We classified all symmetric spaces whose index is less or equal than 3 and symmetric spaces whose rank is equal to their index. In the talk I plan to present these recent results.

© Jurgen Berndt.