{
  "id": "math/0407514",
  "version": "v2",
  "published": "2004-07-29T14:36:48.000Z",
  "updated": "2004-08-02T19:25:23.000Z",
  "title": "Geodesically reversible Finsler 2-spheres of constant curvature",
  "authors": [
    "Robert L. Bryant"
  ],
  "comment": "11 pages, references added, some arguments improved and exposition rearranged",
  "journal": "Inspired by S. S. Chern--A Memorial Volume in Honor of a Great Mathematician, Nankai Tracts in Mathematics, edited by P. A. Griffiths, vol. 11 (Winter, 2006), World Scientific",
  "categories": [
    "math.DG"
  ],
  "abstract": "A Finsler space is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason, it is shown that a geodesically reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily projectively flat. As a corollary, using a previous result of the author, it is shown that a reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily a Riemannian metric of constant Gauss curvature, thus settling a long-standing problem in Finsler geometry.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-08-02T19:25:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C60",
      "53B40"
    ],
    "keywords": [
      "geodesically reversible finsler",
      "constant curvature",
      "constant flag curvature",
      "reversible finsler metric",
      "finsler space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......7514B"
    }
  }
}