{
  "id": "1103.0918",
  "version": "v3",
  "published": "2011-03-04T15:09:28.000Z",
  "updated": "2011-04-14T15:54:32.000Z",
  "title": "On the nullity distribution of the second fundamental form of a submanifold of a space form",
  "authors": [
    "Francisco Vittone"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "If M is a submanifold of a space form, the nullity distribution N of its second fundamental form is (when defined) the common kernel of its shape operators. In this paper we will give a local description of any submanifold of the Euclidean space by means of its nullity distribution. We will also show the following global result: if M is a complete, irreducible submanifold of the Euclidean space or the sphere then N is completely non integrable. This means that any two points in M can be joined by a curve everywhere perpendicular to N. We will finally show that this statement is false for a submanifold of the hyperbolic space.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-04-14T15:54:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "second fundamental form",
      "nullity distribution",
      "space form",
      "euclidean space",
      "common kernel"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.0918V"
    }
  }
}