{
  "id": "1808.04789",
  "version": "v1",
  "published": "2018-08-14T16:49:42.000Z",
  "updated": "2018-08-14T16:49:42.000Z",
  "title": "Some results in $η$-Ricci Soliton and gradient $ρ$-Einstein soliton in a complete Riemannian manifold",
  "authors": [
    "Absos Ali Shaikh",
    "Chandan Kumar Mondal"
  ],
  "comment": "9 pages. We highly appreciate valuable comments from the interested researchers",
  "categories": [
    "math.DG"
  ],
  "abstract": "The main purpose of the paper is to prove that if a compact Riemannian manifold admits a gradient $\\rho$-Einstein soliton such that the gradient Einstein potential is a non-trivial conformal vector field, then the manifold is isometric to the Euclidean sphere. We have showed that a Riemannian manifold satisfying gradient $\\rho$-Einstein soliton with convex Einstein potential possesses non-negative scalar curvature. We have also deduced a sufficient condition for a Riemannian manifold to be compact which satisfies almost $\\eta$-Ricci soliton (see Theorem 2).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-14T16:49:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C15",
      "53C21",
      "53C44",
      "58E20",
      "58J05"
    ],
    "keywords": [
      "complete riemannian manifold",
      "einstein soliton",
      "ricci soliton",
      "einstein potential possesses non-negative",
      "non-trivial conformal vector field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}