{
  "id": "2308.00948",
  "version": "v1",
  "published": "2023-08-02T05:06:32.000Z",
  "updated": "2023-08-02T05:06:32.000Z",
  "title": "Rigidity of Schouten Tensor under Conformal Deformation",
  "authors": [
    "Mijia Lai",
    "Guoqiang Wu"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We obtain some rigidity results for metrics whose Schouten tensor is bounded from below after conformal transformations. Liang Cheng recently proved that a complete, nonflat, locally conformally flat manifold with Ricci pinching condition ($Ric-\\epsilon Rg\\geq 0$) must be compact. This answers higher dimensional Hamilton's pinching conjecture on locally conformally flat manifolds affirmatively. Since (modified) Schouten tensor being nonnegative is equivalent to a Ricci pinching condition, our main result yields a simple proof of Cheng's theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-02T05:06:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schouten tensor",
      "conformal deformation",
      "locally conformally flat manifold",
      "ricci pinching condition",
      "answers higher dimensional hamiltons"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}