{
  "id": "math/0504422",
  "version": "v3",
  "published": "2005-04-21T03:55:31.000Z",
  "updated": "2005-08-29T21:54:03.000Z",
  "title": "On the complex structure of Kähler manifolds with nonnegative curvature",
  "authors": [
    "Albert Chau",
    "Luen-Fai Tam"
  ],
  "comment": ":37 pages, references rearranged, typos corrected",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We study the asymptotic behavior of the K\\\"ahler-Ricci flow on K\\\"ahler manifolds of nonnegative holomorphic bisectional curvature. Using these results we prove that a complete noncompact K\\\"ahler manifold with nonnegative bounded holomorphic bisectional curvature and maximal volume growth is biholomorphic to complex Euclidean space $\\C^n$. We also show that the volume growth condition can be removed if we assume $(M, g)$ has average quadratic scalar curvature decay (see Theorem 2.1) and positive curvature operator.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-08-29T21:54:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C55",
      "35K90"
    ],
    "keywords": [
      "complex structure",
      "kähler manifolds",
      "nonnegative curvature",
      "bounded holomorphic bisectional curvature",
      "average quadratic scalar curvature decay"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4422C"
    }
  }
}