The Signature in Actions of Semisimple Lie Groups on Pseudo-Riemannian Manifolds
DOI:
https://doi.org/10.4067/S0716-09172012000100006Keywords:
Semisimple Lie groups, bi-invariant metric, local freeness, grupos de Lie semisimples, métrica bi-invariante, libertad local.Abstract
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.References
[1] S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, New York, (1978).
[2] M. Gromov, Rigid transformations groups, Geometrie differentielle (Paris 1986), Travaux en Cours 33, Hermann, Paris, pp. 65—139, (1988).
[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).
[5] J. Szaro, Isotropy of semisimple group actions on manifolds with geometric structures, Amer. J. Math.120, pp. 129—158, (1998).
[6] R. J. Zimmer, Ergodic Theory and Semisimple Lie Groups, Birkhauser, Boston, (1984).
[2] M. Gromov, Rigid transformations groups, Geometrie differentielle (Paris 1986), Travaux en Cours 33, Hermann, Paris, pp. 65—139, (1988).
[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).
[5] J. Szaro, Isotropy of semisimple group actions on manifolds with geometric structures, Amer. J. Math.120, pp. 129—158, (1998).
[6] R. J. Zimmer, Ergodic Theory and Semisimple Lie Groups, Birkhauser, Boston, (1984).
Published
2012-01-29
How to Cite
[1]
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.
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