{
  "id": "1606.03187",
  "version": "v1",
  "published": "2016-06-10T05:44:14.000Z",
  "updated": "2016-06-10T05:44:14.000Z",
  "title": "Biharmonic hypersurfaces with constant scalar curvature in space forms",
  "authors": [
    "Yu Fu",
    "Min-Chun Hong"
  ],
  "comment": "16 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $M^n$ be a biharmonic hypersurface with constant scalar curvature in a space form $\\mathbb M^{n+1}(c)$. We show that $M^n$ has constant mean curvature if $c>0$ and $M^n$ is minimal if $c\\leq0$, provided that the number of distinct principal curvatures is no more than 6. This partially confirms Chen's conjecture and Generalized Chen's conjecture. As a consequence, we prove that there exist no proper biharmonic hypersurfaces with constant scalar curvature in Euclidean space $\\mathbb E^{n+1}$ or hyperbolic space $\\mathbb H^{n+1}$ for $n<7$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-10T05:44:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D12"
    ],
    "keywords": [
      "constant scalar curvature",
      "space form",
      "proper biharmonic hypersurfaces",
      "distinct principal curvatures",
      "constant mean curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}