{
  "id": "math/0112166",
  "version": "v1",
  "published": "2001-12-17T11:34:58.000Z",
  "updated": "2001-12-17T11:34:58.000Z",
  "title": "Hyperkähler torsion structures invariant by nilpotent Lie groups",
  "authors": [
    "Isabel G. Dotti",
    "Anna Fino"
  ],
  "comment": "LateX, 12 pages",
  "doi": "10.1088/0264-9381/19/3/309",
  "categories": [
    "math.DG"
  ],
  "abstract": "We study HKT structures on nilpotent Lie groups and on associated nilmanifolds. We exhibit three weak HKT structures on $\\R^8$ which are homogeneous with respect to extensions of Heisenberg type Lie groups. The corresponding hypercomplex structures are of a special kind, called abelian. We prove that on any 2-step nilpotent Lie group all invariant HKT structures arise from abelian hypercomplex structures. Furthermore, we use a correspondence between abelian hypercomplex structures and subspaces of ${\\frak sp}(n)$ to produce continuous families of compact and noncompact of manifolds carrying non isometric HKT structures. Finally, geometrical properties of invariant HKT structures on 2-step nilpotent Lie groups are obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-12-17T11:34:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C26",
      "22E25",
      "81T60"
    ],
    "keywords": [
      "nilpotent lie group",
      "hyperkähler torsion structures invariant",
      "non isometric hkt structures",
      "carrying non isometric hkt",
      "abelian hypercomplex structures"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "IOP",
      "journal": "Class. Quantum Grav."
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}