{
  "id": "2307.13235",
  "version": "v1",
  "published": "2023-07-25T03:55:34.000Z",
  "updated": "2023-07-25T03:55:34.000Z",
  "title": "Non-compact Einstein manifolds with unimodular isometry group",
  "authors": [
    "Christoph Böhm",
    "Ramiro A. Lafuente"
  ],
  "comment": "26 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We show that a negative Einstein manifold admitting a proper isometric action of a connected unimodular Lie group with compact, possibly singular, orbit space splits isometrically as a product of a symmetric space and a compact negative Einstein manifold. The proof involves the theory of polar actions, Lie-theoretic arguments and maximum principles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-25T03:55:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C25",
      "57M60"
    ],
    "keywords": [
      "unimodular isometry group",
      "non-compact einstein manifolds",
      "orbit space splits",
      "compact negative einstein manifold",
      "connected unimodular lie group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}