{
  "id": "1307.5160",
  "version": "v3",
  "published": "2013-07-19T08:36:29.000Z",
  "updated": "2013-09-09T10:32:13.000Z",
  "title": "Killing vector fields of constant length on compact hypersurfaces",
  "authors": [
    "Antonio J. Di Scala"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We show that if a compact hypersurface $M \\subset \\mathbb{R}^{n+1}$, $n \\geq3$, admits a non zero Killing vector field $X$ of constant length then $n$ is even and $M$ is diffeomorphic to the unit hypersphere of $\\mathbb{R}^{n+1}$. Actually, we show that $M$ is a complex ellipsoid in $\\mathbb{C}^{N} = \\mathbb{R}^{n+1}$. As an application we give a simpler proof of a recent theorem due to S. Deshmukh \\cite{De12}.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-09-09T10:32:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "53C22",
      "53C25"
    ],
    "keywords": [
      "constant length",
      "compact hypersurface",
      "non zero killing vector field",
      "unit hypersphere",
      "complex ellipsoid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.5160D"
    }
  }
}