Comptes Rendus
Differential Geometry
Minimal singular Riemannian foliations
[Feuilletages Riemanniens singuliers]
Comptes Rendus. Mathématique, Volume 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

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
@article{CRMATH_2006__342_1_33_0,
     author = {Vicente Miquel and Robert A. Wolak},
     title = {Minimal singular {Riemannian} foliations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {33--36},
     publisher = {Elsevier},
     volume = {342},
     number = {1},
     year = {2006},
     doi = {10.1016/j.crma.2005.10.031},
     language = {en},
}
TY  - JOUR
AU  - Vicente Miquel
AU  - Robert A. Wolak
TI  - Minimal singular Riemannian foliations
JO  - Comptes Rendus. Mathématique
PY  - 2006
SP  - 33
EP  - 36
VL  - 342
IS  - 1
PB  - Elsevier
DO  - 10.1016/j.crma.2005.10.031
LA  - en
ID  - CRMATH_2006__342_1_33_0
ER  - 
%0 Journal Article
%A Vicente Miquel
%A Robert A. Wolak
%T Minimal singular Riemannian foliations
%J Comptes Rendus. Mathématique
%D 2006
%P 33-36
%V 342
%N 1
%I Elsevier
%R 10.1016/j.crma.2005.10.031
%G en
%F CRMATH_2006__342_1_33_0
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/

[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

Cité par 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.

Commentaires - Politique