{
  "id": "1512.05859",
  "version": "v1",
  "published": "2015-12-18T06:27:38.000Z",
  "updated": "2015-12-18T06:27:38.000Z",
  "title": "Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group",
  "authors": [
    "Jih-Hsin Cheng",
    "Hung-Lin Chiu",
    "Jenn-Fang Hwang",
    "Paul Yang"
  ],
  "comment": "28 pages, 6 figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "We study immersed, connected, umbilic hypersurfaces in the Heisenberg group $H_{n}$ with $n$ $\\geq $ $2.$ We show that such a hypersurface, if closed, must be rotationally invariant up to a Heisenberg translation. Moreover, we prove that, among others, Pansu spheres are the only such spheres with positive constant sigma-k curvature up to Heisenberg translations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-18T06:27:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L80",
      "35J70",
      "32V20",
      "53A10",
      "49Q10"
    ],
    "keywords": [
      "heisenberg group",
      "umbilic hypersurfaces",
      "heisenberg translation",
      "positive constant sigma-k curvature",
      "pansu spheres"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}