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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Equifocality of a singular Riemannian foliation
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by Marcos M. Alexandrino and Dirk Töben PDF
Proc. Amer. Math. Soc. 136 (2008), 3271-3280 Request permission

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
  • Email: marcosmalex@yahoo.de
  • Dirk Töben
  • Affiliation: Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln, Germany
  • Email: dtoeben@math.uni-koeln.de
  • 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
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 3271-3280
  • MSC (2000): Primary 53C12; Secondary 57R30
  • DOI: https://doi.org/10.1090/S0002-9939-08-09407-0
  • MathSciNet review: 2407093