{
  "id": "2103.15482",
  "version": "v1",
  "published": "2021-03-29T10:35:23.000Z",
  "updated": "2021-03-29T10:35:23.000Z",
  "title": "Besse conjecture with positive isotropic curvature",
  "authors": [
    "Seungsu Hwang",
    "Gabjin Yun"
  ],
  "comment": "21 pages without figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "The critical point equation arises as a critical point of the total scalar curvature functional defined on the space of constant scalar curvature metrics of a unit volume on a compact manifold. In this equation, there exists a function $f$ on the manifold that satisfies the following $$ (1+f){\\rm Ric} = Ddf + \\frac{nf +n-1}{n(n-1)}sg. $$ It has been conjectured that if $(g, f)$ is a solution of the critical point equation, then $g$ is Einstein and so $(M, g)$ is isometric to a standard sphere. In this paper, we show that this conjecture is true if the given Riemannian metric has positive isotropic curvature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-29T10:35:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C25",
      "53C20"
    ],
    "keywords": [
      "positive isotropic curvature",
      "besse conjecture",
      "constant scalar curvature metrics",
      "total scalar curvature functional",
      "critical point equation arises"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}