{
  "id": "2310.14452",
  "version": "v1",
  "published": "2023-10-22T23:26:42.000Z",
  "updated": "2023-10-22T23:26:42.000Z",
  "title": "Polyharmonic hypersurfaces into complex space forms",
  "authors": [
    "José Miguel Balado-Alves"
  ],
  "comment": "16 pages, 0 figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "We characterize polyharmonic Hopf hypersurfaces with constant principal curvatures as solutions of a fourth-order algebraic equation. We construct six different families of proper polyharmonic hypersurfaces in $ \\mathbb{ C P }^n $, and prove that such solutions cannot exist in $ \\mathbb{ C H }^n $. Moreover, we classify all biharmonic Hopf hypersurfaces with constant principal curvatures in complex space forms and study their stability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-22T23:26:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E20",
      "53C43"
    ],
    "keywords": [
      "complex space forms",
      "constant principal curvatures",
      "biharmonic hopf hypersurfaces",
      "proper polyharmonic hypersurfaces",
      "fourth-order algebraic equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}