A geometric proof of the Karpelevich-Mostow's theorem

Abstract

In this paper we give a geometric proof of the Karpelevich's theorem that asserts that a semisimple Lie subgroup of isometries, of a symmetric space of non compact type, has a totally geodesic orbit. In fact, this is equivalent to a well-known result of Mostow about existence of compatible Cartan decompositions.

Cited by in corpus (3)

• Duality of symmetric spaces and polar actions
• Cohomogeneity one actions on symmetric spaces of noncompact type
• Uniform exponential mixing for congruence covers of convex cocompact hyperbolic manifolds