Equifocality of a singular riemannian foliation

Details Equifocality of a singular riemannian foliation Equifocality of a singular riemannian foliation

2007-04-24

arxiv.org/abs/0704.3251v2

Proceedings of the American Mathematical Society Proc. Amer. Math. Soc. (136) (2008), 3271-3280

Mathematics

Differential Geometry

10 pages. This version contains some misprints corrections and improvements of Corollary 1.6

Scientific paper

A singular foliation on a complete riemannian manifold M is said to be riemannian if each geodesic that is perpendicular at one point to a leaf 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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