no. 1
Differential Geometry
Minimal singular Riemannian foliations
[Feuilletages Riemanniens singuliers]

Présenté par : Étienne Ghys

Miquel, Vicente1 ; Wolak, Robert A.2
1 Departamento de Geometría y Topología, Universidad de Valencia, 46100 Burjassot, Spain
2 Institute of Mathematics, Jagiellonian University, 30-059 Krakow, Poland
Comptes Rendus. Mathématique, Tome 342 (2006) no. 1, pp. 33-36.

Nous prouvons que tout feuilletage singulier sur une variété compacte qu'a une métrique riemannienne feuilletée avec feuilles minimales est régulier.

We prove that a singular foliation on a compact manifold admitting an adapted Riemannian metric for which all leaves are minimal must be regular.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.10.031
Miquel, Vicente 1 ; Wolak, Robert A. 2

1 Departamento de Geometría y Topología, Universidad de Valencia, 46100 Burjassot, Spain
2 Institute of Mathematics, Jagiellonian University, 30-059 Krakow, Poland 
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Miquel, Vicente; Wolak, Robert A. Minimal singular Riemannian foliations. Comptes Rendus. Mathématique, Tome 342 (2006) no. 1, pp. 33-36. doi : 10.1016/j.crma.2005.10.031. http://www.numdam.org/articles/10.1016/j.crma.2005.10.031/

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[2] Masa, X. Duality and minimality in Riemannian foliations, Comment. Math. Helv., Volume 67 (1992), pp. 17-27

[3] Molino, P. Riemannian Foliations, Progr. Math., vol. 73, Birkhäuser, 1988

[4] Sakai, T. Riemannian Geometry, Transl. Math. Monogr., vol. 149, Amer. Math. Soc., 1996

[5] Tondeur, Ph. Geometry of Foliations, Bikhäuser, 1997

[6] Vaisman, I. Lectures on the Geometry of Poisson Manifolds, Progr. Math., vol. 118, Birkhäuser, 1994

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⁎ Partly supported by DGI (Spain) and FEDER Project MTM 2004-06015-C02-01, a sabbatical year from the University of Valencia and by Polish KBN grant 2PO3A021 25.