Proofs of Conjectures about singular riemannian foliations
Abstract
We prove that if the normal distribution of a singular riemannian foliation is integrable, then each leaf of this normal distribution can be extended to be a complete immersed totally geodesic submanifold (called section) which meets every leaf orthogonally. In addition the set of regular points is open and dense in each section. This result generalizes a result of Boualem and solves a problem inspired by a remark of Palais and Terng and a work of Szenthe about polar actions. We also study the singular holonomy of a singular riemannian foliation with sections (s.r.f.s for short) and in particular the transverse orbit of the closure of each leaf. Furthermore we prove that the closure of the leaves of a s.r.f.s. on M form a partition of M which is a singular riemannian foliation. This result proves partially a conjecture of Molino.
Cite
@article{arxiv.math/0509405,
title = {Proofs of Conjectures about singular riemannian foliations},
author = {Marcos M. Alexandrino},
journal= {arXiv preprint arXiv:math/0509405},
year = {2011}
}
Comments
Latex2e; The final publication is available at springerlink.com http://www.springerlink.com/content/q48682633730t831/