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A geometric proof of the Karpelevich–Mostow theorem
Author(s) -
Di Scala Antonio J.,
Olmos Carlos
Publication year - 2009
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdp036
Subject(s) - mathematics , geodesic , pure mathematics , cartan decomposition , lie group , orbit (dynamics) , type (biology) , symmetric space , space (punctuation) , mathematical analysis , computer science , ecology , lie conformal algebra , adjoint representation of a lie algebra , engineering , biology , aerospace engineering , operating system
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.