Polar foliations and isoparametric maps

Details Polar foliations and isoparametric maps Polar foliations and isoparametric maps

2011-02-04

arxiv.org/abs/1102.1018v1

Annals of Global Analysis and Geometry: Volume 41, Issue 2 (2012), Page 187-198

Mathematics

Differential Geometry

9 pages; The final publication is available at springerlink.com http://www.springerlink.com/content/c72g4q5350g513n1/

Scientific paper

10.1007/s10455-011-9277-x

A singular Riemannian foliation $F$ on a complete Riemannian manifold $M$ is called a polar foliation if, for each regular point $p$, there is an immersed submanifold $\Sigma$, called section, that passes through $p$ and that meets all the leaves and always perpendicularly. A typical example of a polar foliation is the partition of $M$ into the orbits of a polar action, i.e., an isometric action with sections. In this work we prove that the leaves of $F$ coincide with the level sets of a smooth map $H: M\to \Sigma$ if $M$ is simply connected. In particular, we have that the orbits of a polar action on a simply connected space are level sets of an isoparametric map. This result extends previous results due to the author and Gorodski, Heintze, Liu and Olmos, Carter and West, and Terng.

Affiliated with

Also associated with

No associations

Rating

Polar foliations and isoparametric maps 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 Polar foliations and isoparametric maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Polar foliations and isoparametric maps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-52331