The Signature in Actions of Semisimple Lie Groups on Pseudo-Riemannian Manifolds


  • José Rosales-Ortega Universidad de Costa Rica



Semisimple Lie groups, bi-invariant metric, local freeness, grupos de Lie semisimples, métrica bi-invariante, libertad local.


We study the relationship between the signature of a semisimple Lie group and a pseudoRiemannian manifold on wich the group acts topologically transitively and isometrically. We also provide a descrip­tion of the bi-invariant pseudo-Riemannian metrics on a semisimple Lie Group over R in terms of the complexification of the Lie algebra associated to the group, and then we utilize it to prove a remark of Gromov.

Author Biography

José Rosales-Ortega, Universidad de Costa Rica

Department of Mathematics.


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[3] B. O’neill, SEMI-RIEMANNIAN GEOMETRY, Academic Press, New York, (1983).

[4] J. Rosales-Ortega, The Gromov’s Centralizer theorem for semisimple Lie group actions. Ph.D. Thesis, CINVESTAV-IPN, (2005).

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[6] R. J. Zimmer, Ergodic Theory and Semisimple Lie Groups, Birkhauser, Boston, (1984).



How to Cite

J. Rosales-Ortega, “The Signature in Actions of Semisimple Lie Groups on Pseudo-Riemannian Manifolds”, Proyecciones (Antofagasta, On line), vol. 31, no. 1, pp. 51-63, Jan. 2012.