{
  "id": "math-ph/0305013",
  "version": "v1",
  "published": "2003-05-07T15:07:31.000Z",
  "updated": "2003-05-07T15:07:31.000Z",
  "title": "Geodesic Flow on the Diffeomorphism Group of the circle",
  "authors": [
    "Adrian Constantin",
    "Boris Kolev"
  ],
  "comment": "15 pages",
  "journal": "Comment. Math. Helv. 78 no 4, pp. 787--804 (2003)",
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We show that certain right-invariant metrics endow the infinite-dimensional Lie group of all smooth orientation-preserving diffeomorphisms of the circle with a Riemannian structure. The study of the Riemannian exponential map allows us to prove infinite-dimensional counterparts of results from classical Riemannian geometry: the Riemannian exponential map is a smooth local diffeomorphism and the length-minimizing property of the geodesics holds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-05-07T15:07:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "58B25"
    ],
    "keywords": [
      "diffeomorphism group",
      "geodesic flow",
      "riemannian exponential map",
      "infinite-dimensional lie group",
      "right-invariant metrics endow"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.2991/jnmp.2003.10.4.1",
      "journal": "Journal of Nonlinear Mathematical Physics",
      "year": 2003,
      "volume": 10,
      "number": 4,
      "pages": 424
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003JNMP...10..424C"
    }
  }
}