Polar actions on Damek-Ricci spaces

6 Aug 2020  ·  Andreas Kollross ·

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. read more

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Differential Geometry 53C30, 53C35, 57S20, 22F30