{
  "id": "math/0701790",
  "version": "v1",
  "published": "2007-01-27T06:00:51.000Z",
  "updated": "2007-01-27T06:00:51.000Z",
  "title": "Deformations in G_2 Manifolds",
  "authors": [
    "Selman Akbulut",
    "Sema Salur"
  ],
  "comment": "13 pages",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "Here we study the deformations of associative submanifolds inside a G_2 manifold M^7 with a calibration 3-form \\phi. A choice of 2-plane field \\Lambda on M (which always exits) splits the tangent bundle of M as a direct sum of a 3-dimensional associate bundle and a complex 4-plane bundle TM= E\\oplus V, and this helps us to relate the deformations to Seiberg-Witten type equations. Here all the surveyed results as well as the new ones about G_2 manifolds are proved by using only the cross product operation (equivalently \\phi). We feel that mixing various different local identifications of the rich G_2 geometry (e.g. cross product, representation theory and the algebra of octonions) makes the study of G_2 manifolds looks harder then it is (e.g. the proof of McLean's theorem \\cite{m}). We believe the approach here makes things easier and keeps the presentation elementary. This paper is essentially self contained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-01-27T06:00:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C38",
      "53C29",
      "57R57"
    ],
    "keywords": [
      "deformations",
      "cross product operation",
      "seiberg-witten type equations",
      "manifolds looks harder",
      "presentation elementary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1790A"
    }
  }
}