{
  "id": "math/0210418",
  "version": "v2",
  "published": "2002-10-27T22:56:19.000Z",
  "updated": "2003-04-11T01:30:48.000Z",
  "title": "Spinors as automorphisms of the tangent bundle",
  "authors": [
    "Alexandru Scorpan"
  ],
  "comment": "19 pages, 1 LaTeX figure. Minor revision, one figure added. To appear in Transaction of the AMS",
  "journal": "Trans. Amer. Math. Soc., vol. 356 (2004), mo. 5, pp. 2049-2066",
  "categories": [
    "math.DG",
    "math.GT"
  ],
  "abstract": "We show that, on a 4-manifold M endowed with a spin^c structure induced by an almost-complex structure, a self-dual (= positive) spinor field \\phi \\in \\Gamma(W^+) is the same as a bundle morphism \\phi: TM \\to TM acting on the fiber by self-dual conformal transformations, such that the Clifford multiplication is just the evaluation of \\phi on tangent vectors, and that the squaring map \\sigma: W^+ \\to \\Lambda^+ acts by pulling-back the fundamental form of the almost-complex structure. We use this to detect Kahler and symplectic structures.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-04-11T01:30:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C27",
      "57N13",
      "32Q60",
      "53D05"
    ],
    "keywords": [
      "tangent bundle",
      "automorphisms",
      "almost-complex structure",
      "self-dual conformal transformations",
      "spinor field"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10418S"
    }
  }
}