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arXiv · 2008.02606

Polar actions on Damek-Ricci spaces

Andreas Kollross
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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.

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Andreas Kollross. 2020-08-06. Polar actions on Damek-Ricci spaces. https://doi.org/10.1016/j.difgeo.2021.101753

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