Submanifolds in Hermitian Symmetric Spaces

Jurgen Berndt - London

Resumo:

A symmetric space is a Riemannian manifold with the property that the geodesic symmetry in each point extends to a globally well defined isometry of the manifold. Symmetric spaces were investigated and classified by Élie Cartan who established a remarkable relationship between symmetric spaces and semisimple Lie groups.

A Kähler manifold is a Riemannian manifold which is equipped with an ortogonal complex structure that is preserved under parallel translation. Kähler manifolds form a classical topic in complex geometry.

Hermitian symmetric spaces arise in the intersection of both topics. in the talk, I plan to discuss some open problems for submanifolds in Hermitian symmetric spaces.

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© Jurgen Berndt.