Differential Geometry/Group Theory
PseudoRiemannian geometry and actions of simple Lie groups
Comptes Rendus. Mathématique, Volume 341 (2005) no. 6, pp. 361-364.

Let G be a connected noncompact simple Lie group acting isometrically on a connected compact pseudoRiemannian manifold M. Denote with n0 and m0 the dimension of the maximal null subspaces tangent to G and M, respectively. Then we always have n0m0. Our main result states that, if n0=m0, then the G-action is, up to a finite covering, an algebraic action. We use this to obtain a complete characterization of a large family of G-actions, thus providing a partial positive answer to the conjecture proposed in Zimmer's program for pseudoRiemannian manifolds.

Soit G un groupe de Lie simple non compact connexe agissant isométriquement sur une variété pseudoRiemannienne compacte connexe M. Dénotez avec n0 et m0 la dimension des sous-espaces nuls maximales tangents á G et M, respectivement. Alors nous avons toujours n0m0. Notre résultat principal déclare que, si n0=m0, alors le action de G est, jusqu'à une revêtement finie, une action algébrique. Nous employons ceci pour obtenir une caractérisation complète d'une famille nombreuse de actions de G, de ce fait fournissant une réponse positive partielle à la conjecture proposé dans le programme de Zimmer pour le variété pseudoRiemannienne.

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DOI: 10.1016/j.crma.2005.08.005
Quiroga-Barranco, Raul 1

1 Centro de Investigaciones en Matemáticas, A.P. 402, Guanajuato, Gto., C.P. 36000, México
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Quiroga-Barranco, Raul. PseudoRiemannian geometry and actions of simple Lie groups. Comptes Rendus. Mathématique, Volume 341 (2005) no. 6, pp. 361-364. doi : 10.1016/j.crma.2005.08.005. http://www.numdam.org/articles/10.1016/j.crma.2005.08.005/

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