{
  "id": "math/0405098",
  "version": "v5",
  "published": "2004-05-06T14:18:58.000Z",
  "updated": "2016-11-08T11:44:36.000Z",
  "title": "Classification of connected holonomy groups of pseudo-Kählerian manifolds of index 2",
  "authors": [
    "Anton S. Galaev"
  ],
  "comment": "This paper has been withdrawn, since the results of this paper are obtained in a much simpler way in arXiv:1606.07701",
  "categories": [
    "math.DG"
  ],
  "abstract": "The problem of classification of connected holonomy groups (equivalently of holonomy algebras) for pseudo-Riemannian manifolds is open. The classification of Riemannian holonomy algebras is a classical result. The classification of Lorentzian holonomy algebras was obtained recently. In the present paper weakly-irreducible not irreducible subalgebras of $\\su(1,n+1)$ ($n\\geq 0$) are classified. Weakly-irreducible not irreducible holonomy algebras of pseudo-K\\\"ahlerian and special pseudo-K\\\"ahlerian manifolds are classified. An example of metric for each possible holonomy algebra is given. This gives the classification of holonomy algebras for pseudo-K\\\"ahlerian manifolds of index 2",
  "revisions": [
    {
      "version": "v4",
      "updated": "2006-12-14T15:13:45.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v5",
      "updated": "2016-11-08T11:44:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C29",
      "53C50",
      "53B30"
    ],
    "keywords": [
      "connected holonomy groups",
      "classification",
      "pseudo-kählerian manifolds",
      "lorentzian holonomy algebras",
      "riemannian holonomy algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5098G"
    }
  }
}