{
  "id": "math/0410180",
  "version": "v2",
  "published": "2004-10-06T17:35:24.000Z",
  "updated": "2004-10-08T17:48:28.000Z",
  "title": "Conformally flat manifolds with nonnegative Ricci curvature",
  "authors": [
    "Gilles Carron",
    "Marc Herzlich"
  ],
  "comment": "revised version, added reference to previous paper by S. Zhu on the same subject",
  "categories": [
    "math.DG"
  ],
  "abstract": "We show that complete conformally flat manifolds of dimension n>2 with nonnegative Ricci curvature enjoy nice rigidity properties: they are either flat, or locally isometric to a product of a sphere and a line, or are globally conformally equivalent to flat space or to a spherical spaceform. This extends previous works by Q.-M. Cheng, M.H. Noronha, B.-L. Chen and X.-P. Zhu, and S. Zhu.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-10-08T17:48:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C15",
      "53C24",
      "58J60"
    ],
    "keywords": [
      "nonnegative ricci curvature",
      "conformally flat manifolds",
      "curvature enjoy nice rigidity properties",
      "ricci curvature enjoy nice rigidity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10180C"
    }
  }
}