{
  "id": "1804.10706",
  "version": "v1",
  "published": "2018-04-27T22:41:47.000Z",
  "updated": "2018-04-27T22:41:47.000Z",
  "title": "Weakly Einstein critical metrics of the volume functional on compact manifolds with boundary",
  "authors": [
    "H. Baltazar",
    "A. Da Silva",
    "F. Oliveira"
  ],
  "comment": "10 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "The goal of this paper is to study weakly Einstein critical metrics of the volume functional on a compact manifold $M$ with smooth boundary $\\partial M$. Here, we prove that an $n$-dimensional, $n=3$ or $4,$ weakly Einstein critical metric of the volume functional with nonnegative scalar curvature must be isometric to a geodesic ball in a simply connected space form $\\mathbb{R}^{n}$ or $\\mathbb{S}^{n}$. Moreover, in the higher dimensional case ($n\\geq5$), we will established a similar result for weakly Einstein critical metric under a suitable constraint on the Weyl tensor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-27T22:41:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "volume functional",
      "compact manifold",
      "study weakly einstein critical metrics",
      "higher dimensional case",
      "geodesic ball"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}