{
  "id": "0707.0338",
  "version": "v2",
  "published": "2007-07-03T05:03:24.000Z",
  "updated": "2007-09-11T17:38:56.000Z",
  "title": "Integral pinched 3-manifolds are space forms",
  "authors": [
    "Giovanni Catino",
    "Zindine Djadli"
  ],
  "comment": "Some misprints in the first version are corrected",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this paper we prove that, under an explicit integral pinching assumption between the $L^2$-norm of the Ricci curvature and the $L^2$-norm of the scalar curvature, a closed 3-manifold with positive scalar curvature admits an Einstein metric with positive curvature. In particular this implies that the manifold is diffeomorphic to a quotient of ${\\Bbb S}^3$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-09-11T17:38:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C24",
      "53C20",
      "53C21",
      "53C25"
    ],
    "keywords": [
      "space forms",
      "explicit integral pinching assumption",
      "positive scalar curvature admits",
      "ricci curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.0338C"
    }
  }
}