On the index of Symmetric Spaces

Jurgen Berndt - Londres

Resumo:

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.

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© Jurgen Berndt.