Desingularization of singular Riemannian foliation

Abstract

Consider a singular Riemannian foliation (s.r.f for short) on a compact manifold. By successive blow-ups along the strata, we construct a regular Riemannian foliation on another compact Riemannian manifold and a desingularization map that projects leaves of the regular Riemannian foliation into leaves of the s.r.f. This result generalizes a previous result due to Molino for the particular case of a singular Riemannian foliation whose leaves were the closure of leaves of a regular Riemannian foliation. We also prove that, if the leaves of the s.r.f are compact, then, for each small epsilon, the regular foliation can be chosen so that the desingularization map induces an epsilon-isometry between the leaf space of the regular Riemannian foliation and the leaf space of the s.r.f. This implies in particular that, the leaf space of the s.r.f is is a Gromov-Hausdorff limit of a sequence of Riemannian orbifolds.

20 pages; The final publication is available at http://www.springerlink.com/content/3973u3q433765n12/

References in corpus (2)

• Proofs of Conjectures about singular riemannian foliations
• Geometric resolution of singular Riemannian foliations

Cited by in corpus (10)

• Progress in the Theory of Singular Riemannian Foliations
• Closure of singular foliations: the proof of Molino's conjecture
• On singular Finsler foliation
• Mean curvature flow of singular Riemannian foliations
• On closed geodesics in the leaf spaces of singular Riemannian foliations
• Smoothness of isometric flows on orbit spaces and applications to the theory of foliations
• Differentiable classification of 4-manifolds with singular Riemannian foliations
• Introduction to Lie groups, isometric and adjoint actions and some generalizations
• On finsler entropy of smooth distributions and Stefan-Sussman foliations
• Leaf closures of Riemannian foliations: a survey on topological and geometric aspects of Killing foliations