{
  "id": "1103.1201",
  "version": "v3",
  "published": "2011-03-07T06:13:59.000Z",
  "updated": "2013-03-24T10:17:49.000Z",
  "title": "Geometric structures associated with a simple Cartan 3-form",
  "authors": [
    "Hong Van Le"
  ],
  "comment": "32 pages, final version, previous wrong Example 3.5 is removed",
  "journal": "Journal of Geometry and Physics (2013)",
  "doi": "10.1016/j.geomphys.2013.03.028",
  "categories": [
    "math.DG"
  ],
  "abstract": "We introduce the notion of a manifold admitting a simple compact Cartan 3-form $\\om^3$. We study algebraic types of such manifolds specializing on those having skew-symmetric torsion, or those associated with a closed or coclosed 3-form $\\om^3$. We prove the existence of an algebra of multi-symplectic forms $\\phi^l$ on these manifolds. Cohomology groups associated with complexes of differential forms on $M^n$ in presence of such a closed multi-symplectic form $\\phi^l$ and their relations with the de Rham cohomologies of $M$ are investigated. We show rigidity of a class of strongly associative (resp. strongly coassociative) submanifolds. We include an appendix describing all connected simply connected complete Riemannian manifolds admitting a parallel 3-form.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-03-24T10:17:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C10",
      "53C38"
    ],
    "keywords": [
      "geometric structures",
      "simple cartan",
      "complete riemannian manifolds admitting",
      "multi-symplectic form",
      "simply connected complete riemannian manifolds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.1201V"
    }
  }
}