{
  "id": "0803.2621",
  "version": "v2",
  "published": "2008-03-18T13:00:39.000Z",
  "updated": "2008-12-09T15:41:29.000Z",
  "title": "Isometric Immersions of Hypersurfaces in 4-dimensional Manifolds via Spinors",
  "authors": [
    "Marie-Amélie Lawn",
    "Julien Roth"
  ],
  "comment": "21 pages, application added",
  "journal": "Differential Geometry and its Applications 28, 2 (2010) 1045-1061",
  "categories": [
    "math.DG"
  ],
  "abstract": "We give a spinorial characterization of isometrically immersed hypersurfaces into 4-dimensional space forms and product spaces $\\M^3(\\kappa)\\times\\R$, in terms of the existence of particular spinor fields, called generalized Killing spinors or equivalently solutions of a Dirac equation. This generalizes to higher dimensions several recent results for surfaces by T. Friedrich, B. Morel and the two authors. The main argument is the interpretation of the energy-momentum tensor of a generalized Killing spinor as the second fundamental form, possibly up to a tensor depending on the ambient space. As an application, we deduce a non-existence result for hypersurfaces in the 4-dimensional Euclidean space.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-12-09T15:41:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C27",
      "53C40",
      "53C80",
      "58C40"
    ],
    "keywords": [
      "isometric immersions",
      "hypersurfaces",
      "generalized killing spinor",
      "second fundamental form",
      "euclidean space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.2621L"
    }
  }
}