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

Ronaldo F. de Lima; Giuseppe Pipoli

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arXiv · 2411.11506

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

Ronaldo F. de Lima·Giuseppe Pipoli

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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.

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Ronaldo F. de Lima, Giuseppe Pipoli. 2024-11-18. Isoparametric Hypersurfaces of $\mathbb H^n\times\mathbb R$ and $\mathbb S^n\times\mathbb R$. https://arxiv.org/abs/2411.11506

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