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Parallel focal structure and singular Riemannian foliations
Author(s):
Dirk
Töben
Journal:
Trans. Amer. Math. Soc.
358
(2006),
1677-1704.
MSC (2000):
Primary 53C12;
Secondary 53C40
Posted:
July 26, 2005
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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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Additional Information:
Dirk
Töben
Affiliation:
Mathematisches Institut, Universität zu Köln, Weyerthal 86-90, 50931 Köln, Germany
Email:
dtoeben@math.uni-koeln.de
DOI:
10.1090/S0002-9947-05-03829-8
PII:
S 0002-9947(05)03829-8
Keywords:
Singular Riemannian foliations,
global foliation,
polar actions,
equifocal submanifolds,
cut locus,
holonomy
Received by editor(s):
June 15, 2004
Posted:
July 26, 2005
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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