{
  "id": "2401.04983",
  "version": "v1",
  "published": "2024-01-10T07:58:04.000Z",
  "updated": "2024-01-10T07:58:04.000Z",
  "title": "The Funk-Finsler structure on the unit disc in the hyperbolic plane",
  "authors": [
    "Ashok Kumar",
    "Hemangi Madhusudan Shah",
    "Bankteshwar Tiwari"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we construct the Funk-Finsler structure in various models of the hyperbolic plane. In particular, in the unit disc of the Klein model, it turns out to be a Randers metric, which is a non-Berwald Douglas metric. Further, using Finsler isometries we obtain the Funk-Finsler structures in other models of the hyperbolic plane. Finally, we also investigate the geometry of this Funk-Finsler metric by explicitly computing the S-curvature, Riemann curvature, flag curvature, and Ricci curvature in the Klein unit disc.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-10T07:58:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperbolic plane",
      "funk-finsler structure",
      "non-berwald douglas metric",
      "klein unit disc",
      "finsler isometries"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}