Comptes Rendus
no. 6
Differential Geometry
Totally geodesic Riemannian foliations with locally symmetric leaves
[Feuilletages riemanniens totalement géodésiques avec des feuilles localement symétriques]

Présenté par : Étienne Ghys

Raul Quiroga-Barranco1, 2
1 Centro de Investigación en Matemáticas, A.C. (CIMAT), A.P. 402, Guanajuato, Gto., C.P. 36000, Mexico
2 Departamento de Matemáticas, CINVESTAV, A.P. 14-740, México, D.F., C.P. 07000, Mexico
Comptes Rendus. Mathématique, Volume 342 (2006) no. 6, pp. 421-426.

Nous prouvons le caractère arithmétique des feuilletages riemanniens totalement géodésiques, possédant une feuille dense, sur une variété riemannienne complète de volume fini, quand les feuilles sont revêtues de façon isométrique par un espace symétrique irréductible de type noncompact et de rang au moins 2.

We prove the arithmeticity of totally geodesic Riemannian foliations, with a dense leaf, on complete finite volume Riemannian manifolds when the leaves are isometrically covered by an irreducible symmetric space of noncompact type and rank at least 2.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.01.015
Raul Quiroga-Barranco 1, 2

1 Centro de Investigación en Matemáticas, A.C. (CIMAT), A.P. 402, Guanajuato, Gto., C.P. 36000, Mexico
2 Departamento de Matemáticas, CINVESTAV, A.P. 14-740, México, D.F., C.P. 07000, Mexico 
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Raul Quiroga-Barranco. Totally geodesic Riemannian foliations with locally symmetric leaves. Comptes Rendus. Mathématique, Volume 342 (2006) no. 6, pp. 421-426. doi : 10.1016/j.crma.2006.01.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.01.015/

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[9] R. Quiroga-Barranco PseudoRiemannian geometry and actions of simple Lie groups, C.R. Math. Acad. Sci. Paris, Ser. I, Volume 341 (2005) no. 6, pp. 361-364

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