Premium
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.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom