Minimal singular Riemannian foliations

Vicente Miquel; Robert A. Wolak

doi:10.1016/j.crma.2005.10.031

Differential Geometry

Minimal singular Riemannian foliations

Presented by: Étienne Ghys

Vicente Miquel ¹; Robert A. Wolak 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, Volume 342 (2006) no. 1, pp. 33-36.

Abstract
Résumé

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: 2005-06-22
Accepted: 2005-10-20
Published online: 2005-11-28

DOI: 10.1016/j.crma.2005.10.031

Author's affiliations:

Vicente Miquel ¹; Robert A. Wolak 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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     title = {Minimal singular {Riemannian} foliations},
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     pages = {33--36},
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     year = {2006},
     doi = {10.1016/j.crma.2005.10.031},
     language = {en},
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Vicente Miquel; Robert A. Wolak. Minimal singular Riemannian foliations. Comptes Rendus. Mathématique, Volume 342 (2006) no. 1, pp. 33-36. doi : 10.1016/j.crma.2005.10.031. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.10.031/

References
Cited by

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

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

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

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

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

[6] I. Vaisman 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.

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