{
  "id": "math/0305139",
  "version": "v1",
  "published": "2003-05-09T14:34:02.000Z",
  "updated": "2003-05-09T14:34:02.000Z",
  "title": "Towards a classification of Lorentzian holonomy groups",
  "authors": [
    "Thomas Leistner"
  ],
  "comment": "73 pages, 3 figures",
  "journal": "J. Differential Geom. 76 (2007), no. 3, 423-484",
  "categories": [
    "math.DG"
  ],
  "abstract": "If the holonomy representation of an $(n+2)$--dimensional simply-connected Lorentzian manifold $(M,h)$ admits a degenerate invariant subspace its holonomy group is contained in the parabolic group $(\\mathbb{R} \\times SO(n))\\ltimes \\mathbb{R}^n$. The main ingredient of such a holonomy group is the SO(n)--projection $G:=pr_{SO(n)}(Hol_p(M,h))$ and one may ask whether it has to be a Riemannian holonomy group. In this paper we show that this is the case if $G\\subset U(n/2)$ or if the irreducible acting components of $G$ are simple.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-05-09T14:34:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53Cxx",
      "53Bxx"
    ],
    "keywords": [
      "lorentzian holonomy groups",
      "classification",
      "riemannian holonomy group",
      "dimensional simply-connected lorentzian manifold",
      "degenerate invariant subspace"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 73,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......5139L"
    }
  }
}