Event Details

Symmetric spaces: Holonomy and totally geodesic submanifolds.

In the 1920s, Élie Cartan asked: which are the Riemannian manifolds whose curvature tensor is invariant under the action of its holonomy group? The answer to this question brought about the notion of symmetric space which arises in a broad diversity of situations in both mathematics and physics. Moreover, totally geodesic submanifolds in symmetric spaces are those submanifolds with the simplest geometry and admit a nice algebraic characterization in terms of Lie algebras. In this talk, I will present a classification of totally geodesic submanifolds in products of symmetric spaces of rank one.