Classification of hypersurfaces with constant principal curvatures in $\mathbb{H}^m\times \mathbb{H}^n$
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Li, Haizhong, Tan, Renhao, Yao, Zeke
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214796411