{
  "id": "1810.06301",
  "version": "v1",
  "published": "2018-10-15T12:18:43.000Z",
  "updated": "2018-10-15T12:18:43.000Z",
  "title": "On compact Riemannian manifolds with harmonic weyl curvature",
  "authors": [
    "Haiping Fu",
    "Huiya He"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We give some rigidity theorems for an n$(\\geq4)$-dimensional compact Riemannian manifold with harmonic Weyl curvature, positive scalar curvature and positive constant $\\sigma_2$. Moreover, when $n=4,$ we prove that a 4-dimensional compact locally conformally flat Riemannian manifold with positive scalar curvature and positive constant $\\sigma_2$ is isometric to a quotient of the round $\\mathbb{S}^4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-15T12:18:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic weyl curvature",
      "positive scalar curvature",
      "dimensional compact riemannian manifold",
      "locally conformally flat riemannian manifold",
      "positive constant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}