{
  "id": "0804.1695",
  "version": "v2",
  "published": "2008-04-10T13:10:39.000Z",
  "updated": "2008-06-03T11:48:50.000Z",
  "title": "Sub-Riemannian geodesics on the 3-D sphere",
  "authors": [
    "Der-Chen Chang",
    "Irina Markina",
    "Alexander Vasil'ev"
  ],
  "comment": "13 pages, 1 figure",
  "categories": [
    "math.DG"
  ],
  "abstract": "The unit sphere $\\mathbb S^3$ can be identified with the unitary group SU(2). Under this identification the unit sphere can be considered as a non-commutative Lie group. The commutation relations for the vector fields of the corresponding Lie algebra define a 2-step sub-Riemannian manifold. We study sub-Riemannian geodesics on this sub-Riemannian manifold making use of the Hamiltonian formalism and solving the corresponding Hamiltonian system.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-06-03T11:48:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C17",
      "70H05"
    ],
    "keywords": [
      "unit sphere",
      "sub-riemannian manifold",
      "unitary group su",
      "corresponding lie algebra define",
      "study sub-riemannian geodesics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.1695C"
    }
  }
}