{
  "id": "0812.4838",
  "version": "v1",
  "published": "2008-12-30T12:47:01.000Z",
  "updated": "2008-12-30T12:47:01.000Z",
  "title": "Compatible structures on Lie algebroids and Monge-Ampère operators",
  "authors": [
    "Yvette Kosmann-Schwarzbach",
    "Vladimir Rubtsov"
  ],
  "comment": "To be published in Acta. Appl. Math, 2009",
  "journal": "Acta Appl. Math., 109 (2010), no. 1, 101-135",
  "categories": [
    "math.DG",
    "math.SG"
  ],
  "abstract": "We study pairs of structures, such as the Poisson-Nijenhuis structures, on the tangent bundle of a manifold or, more generally, on a Lie algebroid or a Courant algebroid. These composite structures are defined by two of the following, a closed 2-form, a Poisson bivector or a Nijenhuis tensor, with suitable compatibility assumptions. We establish the relationships between such composite structures. We then show that the non-degenerate Monge-Amp\\`ere structures on 2-dimensional manifolds satisfying an integrability condition provide numerous examples of such structures, while in the case of 3-dimensional manifolds, such Monge-Amp\\`ere operators give rise to generalized complex structures or generalized product structures on the cotangent bundle of the manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-12-30T12:47:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D17",
      "17B70",
      "58J60",
      "37K10",
      "70G45"
    ],
    "keywords": [
      "lie algebroid",
      "monge-ampère operators",
      "compatible structures",
      "composite structures",
      "nijenhuis tensor"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.4838K"
    }
  }
}