A geometric proof of the Karpelevich-Mostow theorem
A geometric proof of the Karpelevich-Mostow theorem
In this paper we give a geometric proof of 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 the existence of compatible Cartan decompositions.