{
  "id": "math/0610176",
  "version": "v1",
  "published": "2006-10-05T12:38:59.000Z",
  "updated": "2006-10-05T12:38:59.000Z",
  "title": "Flat nearly Kähler manifolds",
  "authors": [
    "Vicente Cortés",
    "Lars Schäfer"
  ],
  "comment": "14 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We classify flat strict nearly K\\\"ahler manifolds with (necessarily) indefinite metric. Any such manifold is locally the product of a flat pseudo-K\\\"ahler factor of maximal dimension and a strict flat nearly K\\\"ahler manifold of split signature $(2m,2m)$ with $m\\ge 3$. Moreover, the geometry of the second factor is encoded in a complex three-form $\\zeta \\in \\Lambda^3 (\\mathbb{C}^m)^*$. The first nontrivial example occurs in dimension $4m=12$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-05T12:38:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C50",
      "53C15"
    ],
    "keywords": [
      "kähler manifolds",
      "first nontrivial example occurs",
      "split signature",
      "indefinite metric",
      "classify flat strict"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10176C"
    }
  }
}