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arXiv · 2609.34876

Classification of hypersurfaces with constant principal curvatures in $\mathbb{H}^m\times \mathbb{H}^n$

Haizhong Li·Renhao Tan·Zeke Yao
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Abstract

In this paper, we study the hypersurfaces in $\mathbb{H}^m\times\mathbb{H}^n$ ($m\geq3, n\geq2$) with constant principal curvatures. Let $g$ be the number of distinct constant principal curvatures. First, we classify all such hypersurfaces with $g\leq2$. Then, we prove that a hypersurface with constant principal curvatures and constant product angle function has $g\le3$, and we obtain a complete classification of these hypersurfaces. As a corollary, we classify the isoparametric hypersurfaces in $\mathbb{H}^m\times \mathbb{H}^n$ ($m\geq3, n\geq2$) with constant principal curvatures.

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Haizhong Li, Renhao Tan, Zeke Yao. 2026-09-28. Classification of hypersurfaces with constant principal curvatures in $\mathbb{H}^m\times \mathbb{H}^n$. https://arxiv.org/abs/2609.34876

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