Progress in the Theory of Singular Riemannian Foliations

Details Progress in the Theory of Singular Riemannian Foliations Progress in the Theory of Singular Riemannian Foliations

2012-03-30

arxiv.org/abs/1203.6829v1

Mathematics

Differential Geometry

Scientific paper

A singular foliation is called a singular Riemannian foliation (SRF) if every geodesic that is perpendicular to one leaf is perpendicular to every leaf it meets. A typical example is the partition of a complete Riemannian manifold into orbits of an isometric action. In this survey, we provide an introduction to the theory of SRFs, leading from the foundations to recent developments in research on this subject. Sketches of proofs are included and useful techniques are emphasized. We study the local structure of SRFs in general and under curvature conditions. We review the solution of the Palais-Terng problem on integrability of the horizontal distribution. Important special classes of SRFs, like polar and variationally complete foliations and their connections, are treated. A characterisation of SRFs whose leaf space is an orbifold is given. Moreover, desingularizations of SRFs are studied and applications, e.g., to Molino's conjecture, are presented.

Affiliated with

Also associated with

No associations

Rating

Progress in the Theory of Singular Riemannian Foliations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Progress in the Theory of Singular Riemannian Foliations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Progress in the Theory of Singular Riemannian Foliations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-64678