{
  "id": "math/0605360",
  "version": "v2",
  "published": "2006-05-14T06:32:06.000Z",
  "updated": "2013-01-06T08:50:53.000Z",
  "title": "New gap theorem on complete Riemannian manifolds",
  "authors": [
    "Qi-hua Ruan"
  ],
  "comment": "This paper has been withdrawn by the author due to some crucial errors",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this short note, we find a new gap phenomena on Riemannian manifolds, which says that for any complete noncompact Riemannian manifold with nonnegative Ricci curvature, if the scalar curvature decays faster than quadratically, then it is Ricci flat.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-01-06T08:50:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "53C21"
    ],
    "keywords": [
      "complete riemannian manifolds",
      "gap theorem",
      "scalar curvature decays faster",
      "complete noncompact riemannian manifold",
      "gap phenomena"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}