{
  "id": "math/0406397",
  "version": "v3",
  "published": "2004-06-21T09:55:25.000Z",
  "updated": "2013-12-09T19:36:15.000Z",
  "title": "Note on the holonomy groups of pseudo-Riemannian manifolds",
  "authors": [
    "Anton S. Galaev"
  ],
  "comment": "6 pages, final version",
  "journal": "Mathematical Notes 93 (2013), no. 5--6, pp. 810--815",
  "categories": [
    "math.DG"
  ],
  "abstract": "For an arbitrary subalgebra $\\mathfrak{h}\\subset\\mathfrak{so}(r,s)$, a polynomial pseudo-Riemannian metric of signature $(r+2,s+2)$ is constructed, the holonomy algebra of this metric contains $\\mathfrak{h}$ as a subalgebra. This result shows the essential distinction of the holonomy algebras of pseudo-Riemannian manifolds of index bigger or equal to 2 from the holonomy algebras of Riemannian and Lorentzian manifolds.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-12-09T19:36:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53B30",
      "53C29",
      "53C50"
    ],
    "keywords": [
      "pseudo-riemannian manifolds",
      "holonomy groups",
      "holonomy algebra",
      "polynomial pseudo-riemannian metric",
      "essential distinction"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6397G"
    }
  }
}