{
  "id": "2107.04210",
  "version": "v1",
  "published": "2021-07-09T04:58:44.000Z",
  "updated": "2021-07-09T04:58:44.000Z",
  "title": "Non-compact Einstein manifolds with symmetry",
  "authors": [
    "Christoph Böhm",
    "Ramiro A. Lafuente"
  ],
  "comment": "57 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "For Einstein manifolds with negative scalar curvature admitting an isometric action of a Lie group G with compact, smooth orbit space, we show the following rigidity result: The nilradical N of G acts polarly, and the N-orbits can be extended to minimal Einstein submanifolds. As an application, we prove the Alekseevskii conjecture: Any homogeneous Einstein manifold with negative scalar curvature is diffeomorphic to a Euclidean space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-09T04:58:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C25",
      "53C30",
      "14L24",
      "57S20"
    ],
    "keywords": [
      "non-compact einstein manifolds",
      "negative scalar curvature",
      "minimal einstein submanifolds",
      "smooth orbit space",
      "homogeneous einstein manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}