AI 中文总结
本文对双曲空间乘积中具有常主曲率的超曲面进行分类，证明了常乘积角函数情形下主曲率个数至多为3，并给出完整分类及等参超曲面的推论。
AI 中文摘要
本文研究了 $\mathbb{H}^m\times\mathbb{H}^n$（$m\geq3, n\geq2$）中具有常主曲率的超曲面。设 $g$ 为互不相同的常主曲率的个数。首先，我们分类了所有满足 $g\leq2$ 的此类超曲面。然后，我们证明了具有常主曲率和常乘积角函数的超曲面满足 $g\le3$，并获得了这些超曲面的完整分类。作为推论，我们分类了 $\mathbb{H}^m\times \mathbb{H}^n$（$m\geq3, n\geq2$）中具有常主曲率的等参超曲面。
英文摘要
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.
Comments39 pages. Comments are welcome
