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PreprintCC BY 4.0arXiv

Classification of hypersurfaces with constant principal curvatures in ℍm× ℍn

  • Haizhong Li
  • Renhao Tan
  • Zeke Yao
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Abstract

In this paper, we study the hypersurfaces in ℍm×ℍn (m≥3, n≥2) with constant principal curvatures. Let g be the number of distinct constant principal curvatures. First, we classify all such hypersurfaces with g≤2. Then, we prove that a hypersurface with constant principal curvatures and constant product angle function has g≤3, and we obtain a complete classification of these hypersurfaces. As a corollary, we classify the isoparametric hypersurfaces in ℍm× ℍn (m≥3, n≥2) with constant principal curvatures.

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Cite

BibTeXRIS
BibTeX
@misc{li2026classification,
  title = {{Classification of hypersurfaces with constant principal curvatures in $\mathbbH^m\times \mathbbH^n$}},
  author = {Haizhong Li and Renhao Tan and Zeke Yao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34876},
  eprint = {2609.34876},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34876},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Classification of hypersurfaces with constant principal curvatures in ℍ^m× ℍ^n
AU  - Haizhong Li
AU  - Renhao Tan
AU  - Zeke Yao
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34876
UR  - https://arxiv.org/abs/2609.34876
AB  - In this paper, we study the hypersurfaces in ℍ^m×ℍ^n (m≥3, n≥2) with constant principal curvatures. Let g be the number of distinct constant principal curvatures. First, we classify all such hypersurfaces with g≤2. Then, we prove that a hypersurface with constant principal curvatures and constant product angle function has g≤3, and we obtain a complete classification of these hypersurfaces. As a corollary, we classify the isoparametric hypersurfaces in ℍ^m× ℍ^n (m≥3, n≥2) with constant principal curvatures.
ER  -