Isoparametric Hypersurfaces of $\mathbb H^n\times\mathbb R$ and $\mathbb S^n\times\mathbb R$

Abstract

We classify the isoparametric hypersurfaces and the homogeneous hypersurfaces of $\mathbb H^n\times\mathbb R$ and $\mathbb S^n\times\mathbb R$, $n\ge 2$, by establishing that any such hypersurface has constant angle function and constant principal curvatures.