A geometric proof of the Karpelevich-Mostow's theorem
Antonio J. Di Scala, Carlos Enrique Olmos · PORTO Publications Open Repository TOrino (Politecnico di Torino) · 2007
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.