{
  "id": "0705.0710",
  "version": "v2",
  "published": "2007-05-07T14:29:01.000Z",
  "updated": "2007-05-30T19:47:07.000Z",
  "title": "On Conformally Kaehler, Einstein Manifolds",
  "authors": [
    "Xiuxiong Chen",
    "Claude LeBrun",
    "Brian Weber"
  ],
  "comment": "45 pages, 9 figures. Simplified proof of Lemma 25. Several minor corrections to section 5",
  "categories": [
    "math.DG",
    "gr-qc",
    "math.AG",
    "math.AP"
  ],
  "abstract": "We prove that any compact complex surface with positive first Chern class admits an Einstein metric which is conformally related to a Kaehler metric. The key new ingredient is the existence of such a metric on the blow-up of the complex projective plane at two distinct points.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-05-30T19:47:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C25",
      "53C55"
    ],
    "keywords": [
      "einstein manifolds",
      "conformally kaehler",
      "compact complex surface",
      "positive first chern class admits",
      "einstein metric"
    ],
    "publication": {
      "journal": "Journal of the American Mathematical Society",
      "year": 2008,
      "month": "Oct",
      "volume": 21,
      "number": 4,
      "pages": 1137
    },
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 750060,
      "adsabs": "2008JAMS...21.1137C"
    }
  }
}