{
  "id": "0802.0950",
  "version": "v1",
  "published": "2008-02-07T11:42:12.000Z",
  "updated": "2008-02-07T11:42:12.000Z",
  "title": "The curvature of contact structure on 3-manifolds",
  "authors": [
    "Vladimir Krouglov"
  ],
  "comment": "9 pages",
  "categories": [
    "math.DG",
    "math.GT"
  ],
  "abstract": "We study the sectional curvature of plane distributions on 3-manifolds. We show that if the distribution is a contact structure it is easy to manipulate this curvature. As a corollary we obtain that for every transversally oriented contact structure on a closed 3-dimensional manifold $M$ there is a metric, such that the sectional curvature of the contact distribution is equal to -1. We also introduce the notion of Gaussian curvature of the plane distribution. For this notion of curvature we get the similar results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-02-07T11:42:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D35",
      "53B21"
    ],
    "keywords": [
      "sectional curvature",
      "plane distribution",
      "similar results",
      "contact distribution",
      "gaussian curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.0950K"
    }
  }
}