{
  "id": "1606.04859",
  "version": "v1",
  "published": "2016-06-15T16:57:53.000Z",
  "updated": "2016-06-15T16:57:53.000Z",
  "title": "Reducibility in Sasakian Geometry",
  "authors": [
    "Charles P. Boyer",
    "Hongnian Huang",
    "Eveline Legendre",
    "Christina W. Tønnesen-Friedman"
  ],
  "comment": "58 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "The purpose of this paper is to study reducibility properties in Sasakian geometry. First we give the Sasaki version of the de Rham Decomposition Theorem; however, we need a mild technical assumption on the Sasaki automorphism group which includes the toric case. Next we introduce the concept of {\\it cone reducible} and consider $S^3$ bundles over a smooth projective algebraic variety where we give a classification result concerning contact structures admitting the action of a 2-torus of Reeb type. In particular, we can classify all such Sasakian structures up to contact isotopy on $S^3$ bundles over a Riemann surface of genus greater than zero. Finally, we show that in the toric case an extremal Sasaki metric on a Sasaki join always splits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-15T16:57:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C25"
    ],
    "keywords": [
      "sasakian geometry",
      "concerning contact structures admitting",
      "classification result concerning contact structures",
      "toric case",
      "smooth projective algebraic variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 58,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}