Totally geodesic submanifolds in compact Riemannian symmetric spaces and their stability (Q1609566)

Using the theory of involutive automorphisms of Lie groups and Lie algebras, the author determines totally geodesic submanifolds of compact symmetric spaces. He gives necessary and sufficient conditions for these submanifolds to be polars or meridians. With the help of Ohnita's formula and representation theory of Lie groups, the stability of such submanifolds is determined. For simplicity and conciseness, the only exceptional compact Riemannian symmetric spaces are discussed.