Foliation by G-orbits

  • Jose Rosales-Ortega University of Costa Rica
Keywords: semisimple Lie groups, Riemannian foliation, local freeness

Abstract

We study the properties of the normal bundle defined by the bundle of the G-orbits of the action of a semisimple Lie group G on a pseudo Riemannian manifold M, as a consequence we obtain that the foliation induced by the normal bundle is integrable and totally geodesic.

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Author Biography

Jose Rosales-Ortega, University of Costa Rica

Department of Mathematics

Professor.

References

S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, New York, 1978.

M. Gromov, Rigid transformations groups, Géométrie différentielle (Paris 1986), Travaux en Cours 33, Hermann, Paris, 1988, pp. 65-139.

S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, vol. I, John Wiley & Sons, New York, 1963.

P. Molino, Riemannian Foliations, Progress in Mathematics Volume 73. Birkhäuser, 1988.

B. O'Neill, SEMI-RIEMANNIAN GEOMETRY, Academic Press, New York, 1983.

B. O'Neill, The Fundamental Equations of a Submersion, Michigan Math. Journal, 13, 459-469,(1966).

J. Rosales-Ortega, The Gromov's Centralizer Theorem for Semisimple Lie Group Actions, Ph.D thesis(2005), Cinvestav-IPN, Mexico City, Mexico.

J. Rosales-Ortega, The Signature in actions of Semisimple Lie Group on pseudo-Riemannian manifolds, Proyecciones Journal of Mathematics. 31, 51-63, (2012).

J. Szaro, Isotropy of semisimple group actions on manifolds with geometric structures, Amer. J. Math.120, 129-158(1990).

R. J. Zimmer, Ergodic Theory and Semisimple Lie Groups, Birkhäuser, Boston, 1984.

R. J. Zimmer, On the automorphism group of a compact Lorentz manifold and other geometric manifolds, Invent. Math. 83, 411-424, (1986).

R. J. Zimmer, Automorphism groups and fundamental group of geometric manifold, Proceedings of Symposia in Pure Mathematics. 54, 693-710,(1993).

Published
2014-08-10
Section
Articles