Polar actions on Damek-Ricci spaces |
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Affiliation: | Institut für Geometrie und Topologie, Universität Stuttgart, Germany |
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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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Keywords: | Damek-Ricci space Polar action |
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