Differential Geometry
Minimal singular Riemannian foliations
Comptes Rendus. Mathématique, Volume 342 (2006) no. 1, pp. 33-36.

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

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

Received:
Accepted:
Published online:
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, Volume 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/

[1] Haefliger, A. Some remarks on foliations with minimal leaves, J. Differential Geom., Volume 15 (1980), pp. 269-284

[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

Cited by Sources:

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.