{
  "id": "math/0702790",
  "version": "v3",
  "published": "2007-02-26T16:57:29.000Z",
  "updated": "2007-10-11T08:29:28.000Z",
  "title": "Torsion of SU(2)-structures and Ricci curvature in dimension 5",
  "authors": [
    "Lucio Bedulli",
    "Luigi Vezzoni"
  ],
  "comment": "18 pages, The main formula has been corrected",
  "journal": "Differential Geom. Appl. 27 (2009), no. 1, 85-99",
  "categories": [
    "math.DG"
  ],
  "abstract": "In anlogy with the work of R. Bryant on the Ricci tensor of a G$_2$-structure, we study the intrinsic torsion of an SU$(2)$-structure on a 5-dimensional manifold deriving an explicit expression for the Ricci and the scalar curvature in terms of torsion forms and its derivative. As a consequence of this formula we prove that the $\\alpha$-Einstein condition forces some special SU(2)-structures to be Sasaki-Einstein.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-10-11T08:29:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C10",
      "53C25",
      "53C15",
      "53D15"
    ],
    "keywords": [
      "ricci curvature",
      "einstein condition forces",
      "explicit expression",
      "ricci tensor",
      "torsion forms"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2790B"
    }
  }
}