Isoparametric functions on ${\mathbb{R}}^n\times {\mathbb{M}}^m$

Abstract

We classify the isoparametric functions on ${\mathbb{R}}^n\times {\mathbb{M}}^m$, $n,m\ge 2$, with compact level sets, where ${\mathbb{M}}^m$ is a connected, closed Riemannian manifold of dimension $m$. Also, we classify the isoparametric hypersurfaces in ${\mathbb{S}}^2\times {\mathbb{R}}^2$ with constant principal curvatures.

arXiv comment10 pages