{
  "id": "math/9911093",
  "version": "v2",
  "published": "1999-11-13T20:09:24.000Z",
  "updated": "2000-08-03T00:53:48.000Z",
  "title": "Calibrated Fibrations",
  "authors": [
    "Edward Goldstein"
  ],
  "comment": "28 pages",
  "categories": [
    "math.DG",
    "math.AG"
  ],
  "abstract": "In this paper we investigate the geometry of Calibrated submanifolds and study relations between their moduli-space and geometry of the ambient manifold. In particular for a Calabi-Yau manifold we define Special Lagrangian submanifolds for any Kahler metric on it. We show that for a choice of Kahler metric the Borcea-Voisin threefold has a fibration structure with generic fiber being a Special Lagrangian torus. Moreover we construct a mirror to this fibration. Also for any closed G_2 form on a 7-manifold we study coassociative submanifolds and we show that one example of a G_2 manifold constructed by Joyce in [10] is a fibration with generic fiber being a coassociative 4-torus. Similarly we construct a mirror to this fibration.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2000-08-03T00:53:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "calibrated fibrations",
      "generic fiber",
      "define special lagrangian submanifolds",
      "kahler metric",
      "special lagrangian torus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....11093G"
    }
  }
}