{
  "id": "2003.05234",
  "version": "v1",
  "published": "2020-03-11T11:49:26.000Z",
  "updated": "2020-03-11T11:49:26.000Z",
  "title": "Compact gradient $ρ$-Einstein soliton is isometric to the Euclidean sphere",
  "authors": [
    "Absos Ali Shaikh",
    "Chandan Kumar Mondal",
    "Prosenjit Mandal"
  ],
  "comment": "6 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper we have investigated some aspects of gradient $\\rho$-Einstein Ricci soliton in a complete Riemannian manifold. First, we have proved that the compact gradient $\\rho$-Einstein soliton is isometric to the Euclidean sphere by showing that the scalar curvature becomes constant. Second, we have showed that in a non-compact gradient $\\rho$-Einstein soliton satisfying some integral condition, the scalar curvature vanishes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-11T11:49:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "53C21",
      "53C44"
    ],
    "keywords": [
      "einstein soliton",
      "euclidean sphere",
      "complete riemannian manifold",
      "scalar curvature vanishes",
      "einstein ricci soliton"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}