{
  "id": "math/0410065",
  "version": "v1",
  "published": "2004-10-04T21:08:34.000Z",
  "updated": "2004-10-04T21:08:34.000Z",
  "title": "Killing forms on G2 and Spin7 manifolds",
  "authors": [
    "Uwe Semmelmann"
  ],
  "comment": "15 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "Killing forms on Riemannian manifolds are differential forms whose covariant derivative is totally skew-symmetric. We show that on a compact manifold with holonomy G2 or Spin7 any Killing form has to be parallel. The main tool is a universal Weitzenboeck formula. We show how such a formula can be obtained for any given holonomy group and any representation defining a vector bundle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-10-04T21:08:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C55"
    ],
    "keywords": [
      "killing form",
      "spin7 manifolds",
      "universal weitzenboeck formula",
      "main tool",
      "vector bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10065S"
    }
  }
}