{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34876",
  "author_total": 3,
  "authors": [
    {
      "name": "Haizhong Li"
    },
    {
      "name": "Renhao Tan"
    },
    {
      "name": "Zeke Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8xdxcb70hey0k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34876",
  "fulltext_url": null,
  "id": "8xdxcb70hey0k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34876",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7214796411",
  "pdf_url": "https://arxiv.org/pdf/2609.34876",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8xdxcb70hey0k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34876",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34876"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Classification of hypersurfaces with constant principal curvatures in $\\mathbb{H}^m\\times \\mathbb{H}^n$",
  "title_text": "Classification of hypersurfaces with constant principal curvatures in ℍ^m× ℍ^n",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/8xdxcb70hey0k",
  "venue": "arXiv",
  "versions": []
}