Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Parallel focal structure and singular Riemannian foliations

Author: Dirk Töben
Journal: Trans. Amer. Math. Soc. 358 (2006), 1677-1704
MSC (2000): Primary 53C12; Secondary 53C40
Published electronically: July 26, 2005
MathSciNet review: 2186992
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Abstract: We give a necessary and sufficient condition for a submanifold with parallel focal structure to give rise to a global foliation of the ambient space by parallel and focal manifolds. We show that this is a singular Riemannian foliation with complete orthogonal transversals. For this object we construct an action on the transversals that generalizes the Weyl group action for polar actions.

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

Keywords: Singular Riemannian foliations, global foliation, polar actions, equifocal submanifolds, cut locus, holonomy
Received by editor(s): June 15, 2004
Published electronically: July 26, 2005
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.