{
  "id": "1010.0238",
  "version": "v1",
  "published": "2010-10-01T19:03:39.000Z",
  "updated": "2010-10-01T19:03:39.000Z",
  "title": "On Einstein, Hermitian 4-Manifolds",
  "authors": [
    "Claude LeBrun"
  ],
  "comment": "33 pages, 3 figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let (M,h) be a compact 4-dimensional Einstein manifold, and suppose that h is Hermitian with respect to some complex structure J on M. Then either (M,J,h) is Kaehler-Einstein, or else, up to rescaling and isometry, it is one of the following two exceptions: the Page metric on CP2 # (-CP2), or the Einstein metric on CP2 # 2 (-CP2) constructed in Chen-LeBrun-Weber.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-01T19:03:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C25",
      "53C55",
      "14M25",
      "35B44"
    ],
    "keywords": [
      "einstein manifold",
      "complex structure",
      "page metric",
      "einstein metric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.0238L"
    }
  }
}