{
  "id": "math/0610532",
  "version": "v1",
  "published": "2006-10-17T21:07:36.000Z",
  "updated": "2006-10-17T21:07:36.000Z",
  "title": "SU(3)-structures and Special Lagrangian Geometries",
  "authors": [
    "Feng Xu"
  ],
  "comment": "31 pages",
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We generalize Calabi-Yau 3-folds from the special Lagrangian perspective. More precisely, we study SU(3)-structures which admit as \"nice\" a local special Lagrangian geometry as the flat $\\mathbf{C}^3$ or a Calabi-Yau structure does. The underlying almost complex structure may not be integrable. Such SU(3)-structures are called {\\it admissible}. Among these, we are particularly interested in a subclass of SU(3)-structures called {\\it nearly Calabi-Yau}. We discuss the local generalities of admissible SU(3)-structures and nearly Calabi-Yau structures in Cartan's sense. Examples of nearly Calabi-Yau but non-Calabi-Yau structures as well as other admissible SU(3)-structures are constructed from the twistor spaces of self-dual Einstein 4-manifolds. Two classes of examples of complete special Lagrangian submanifolds are found by considering the anti-complex involution of the underlying SU(3)-structures. We finally show that the moduli space of compact special Lagrangian submanifolds in a nearly Calabi-Yau manifold behaves in the same way as the moduli in the Calabi-Yau case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-17T21:07:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C38"
    ],
    "keywords": [
      "compact special lagrangian submanifolds",
      "calabi-yau structure",
      "local special lagrangian geometry",
      "complete special lagrangian submanifolds",
      "calabi-yau manifold behaves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10532X"
    }
  }
}