{
  "id": "math/0604608",
  "version": "v2",
  "published": "2006-04-27T19:51:47.000Z",
  "updated": "2008-04-30T12:55:04.000Z",
  "title": "Hermitian structures on cotangent bundles of four dimensional solvable Lie groups",
  "authors": [
    "L. C. de Andrés",
    "M. L. Barberis",
    "I. Dotti",
    "M. Fernández"
  ],
  "comment": "26 pages. Typos corrected",
  "journal": "Osaka J. Math. 44, 765--793, 2007",
  "categories": [
    "math.DG"
  ],
  "abstract": "We study hermitian structures, with respect to the standard neutral metric on the cotangent bundle $T^*G$ of a 2n-dimensional Lie group $G$, which are left invariant with respect to the Lie group structure on $T^*G$ induced by the coadjoint action. These are in one-to-one correspondence with left invariant generalized complex structures on $G$. Using this correspondence and results of Cavalcanti-Gualtieri and Fern\\'andez-Gotay-Gray, it turns out that when $G$ is nilpotent and four or six dimensional, the cotangent bundle $T^*G$ always has a hermitian structure. However, we prove that if $G$ is a four dimensional solvable Lie group admitting neither complex nor symplectic structures, then $T^*G$ has no hermitian structure or, equivalently, $G$ has no left invariant generalized complex structure.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-04-30T12:55:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B30",
      "53C15",
      "22E25",
      "53C55",
      "53D17"
    ],
    "keywords": [
      "dimensional solvable lie group",
      "hermitian structure",
      "cotangent bundle",
      "left invariant generalized complex structure"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}