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

Rosales-Ortega, José ^[1]
1. [1] Universidad de Costa Rica
  
  Universidad de Costa Rica
  
  Hospital, Costa Rica
Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 31, Nº. 1, 2012, págs. 51-63
Idioma: inglés
DOI: 10.4067/S0716-09172012000100006
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Resumen
- 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.
Referencias bibliográficas
- Citas [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).