Polar actions on Damek-Ricci spaces
Differential Geometry
2021-03-19 v2
Abstract
A proper isometric Lie group action on a Riemannian manifold is called polar if there exists a closed connected submanifold which meets all orbits orthogonally. In this article we study polar actions on Damek-Ricci spaces. We prove criteria for isometric actions on Damek-Ricci spaces to be polar, find examples and give some partial classifications of polar actions on Damek-Ricci spaces. In particular, we show that non-trivial polar actions exist on all Damek-Ricci spaces.
Keywords
Cite
@article{arxiv.2008.02606,
title = {Polar actions on Damek-Ricci spaces},
author = {Andreas Kollross},
journal= {arXiv preprint arXiv:2008.02606},
year = {2021}
}
Comments
v1: 14 pages; v2: 15 pages, Lemma 3.6 and Theorem 3.7 corrected, minor changes