{
  "id": "math/0304092",
  "version": "v1",
  "published": "2003-04-07T09:51:39.000Z",
  "updated": "2003-04-07T09:51:39.000Z",
  "title": "Some integrability conditions for almost Kähler manifolds",
  "authors": [
    "Klaus-Dieter Kirchberg"
  ],
  "comment": "Latex2e, 13 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "Among other results, a compact almost K\\\"ahler manifold is proved to be K\\\"ahler if the Ricci tensor is semi-negative and its length coincides with that of the star Ricci tensor or if the Ricci tensor is semi-positive and its first order covariant derivatives are Hermitian. Moreover, it is shown that there are no compact almost K\\\"ahler manifolds with harmonic Weyl tensor and non-parallel semi-positive Ricci tensor. Stronger results are obtained in dimension 4.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-04-07T09:51:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53B20",
      "53C25"
    ],
    "keywords": [
      "kähler manifolds",
      "integrability conditions",
      "first order covariant derivatives",
      "star ricci tensor",
      "non-parallel semi-positive ricci tensor"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}