{
  "id": "math/0612655",
  "version": "v1",
  "published": "2006-12-21T16:42:03.000Z",
  "updated": "2006-12-21T16:42:03.000Z",
  "title": "Homogeneous nearly Kähler manifolds",
  "authors": [
    "Jean-Baptiste Butruille"
  ],
  "comment": "This is the english version of an older article written in french (Classification des vari\\'{e}t\\'{e}s approximativement k\\\"{a}hleriennes homog\\`{e}nes, Ann. Global Anal. Geom. 27, 201-225, 2005). It contains no new results. However, we modified the structure of the paper, simplified some proofs and added a lot of explanations, especially on 3-symmetric spaces. It can be read as a sort of survey on nearly K\\\"{a}hler manifolds",
  "categories": [
    "math.DG"
  ],
  "abstract": "We classify six-dimensional homogeneous nearly K\\\"{a}hler manifolds and give a positive answer to Gray and Wolf's conjecture: every homogeneous nearly K\\\"{a}hler manifold is a Riemannian 3-symmetric space equipped with its canonical almost Hermitian structure. The only four examples in dimension 6 are $S^3 \\times S^3$, the complex projective space $\\CM P^3$, the flag manifold $\\mathbb F^3$ and the sphere $S^6$. We develop, about each of these spaces, a distinct aspect of nearly K\\\"{a}hler geometry and make in the same time a sharp description of its specific homogeneous structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-12-21T16:42:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C10",
      "53C15",
      "53C25",
      "53C28",
      "53C30"
    ],
    "keywords": [
      "kähler manifolds",
      "hermitian structure",
      "specific homogeneous structure",
      "wolfs conjecture",
      "complex projective space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "fr",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12655B"
    }
  }
}