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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Equifocality of a singular Riemannian foliation

Authors: Marcos M. Alexandrino and Dirk Töben
Journal: Proc. Amer. Math. Soc. 136 (2008), 3271-3280
MSC (2000): Primary 53C12; Secondary 57R30
Published electronically: April 23, 2008
MathSciNet review: 2407093
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Abstract: A singular foliation on a complete Riemannian manifold $ M$ is said to be Riemannian if each geodesic that is perpendicular to a leaf at one point remains perpendicular to every leaf it meets. We prove that the regular leaves are equifocal, i.e., the end point map of a normal foliated vector field has constant rank. This implies that we can reconstruct the singular foliation by taking all parallel submanifolds of a regular leaf with trivial holonomy. In addition, the end point map of a normal foliated vector field on a leaf with trivial holonomy is a covering map. These results generalize previous results of the authors on singular Riemannian foliations with sections.

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Additional Information

Marcos M. Alexandrino
Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010,05508 090 São Paulo, Brazil

Dirk Töben
Affiliation: Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln, Germany

PII: S 0002-9939(08)09407-0
Keywords: Singular Riemannian foliations, equifocal submanifolds, isometric actions
Received by editor(s): May 25, 2007
Published electronically: April 23, 2008
Additional Notes: The first author was supported by CNPq and partially supported by FAPESP
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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