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Bulletin of the London Mathematical Society Advance Access originally published online on May 12, 2009
Bulletin of the London Mathematical Society 2009 41(4):634-638; doi:10.1112/blms/bdp036
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© 2009 London Mathematical Society

A geometric proof of the Karpelevich–Mostow theorem

Antonio J. Di Scala

Dipartimento di Matematica
Politecnico di Torino
Corso Duca degli Abruzzi 24
10129 Torino
Italy

Carlos Olmos

Fa.M.A.F.
Universidad Nacional de Córdoba
Ciudad Universitaria
5000 Cordoba
Argentina
olmos@mate.uncor.edu

Received 8 February 2008. Revision received 27 January 2009.

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.

2000 Mathematics Subject Classification 53C35 (primary), 53C30, 53C40, 53C42 (secondary).

Research supported by Programa Raices, Subsidio Cesar Milstein, Republica Argentina.


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