{
  "id": "1611.09109",
  "version": "v1",
  "published": "2016-11-28T13:25:33.000Z",
  "updated": "2016-11-28T13:25:33.000Z",
  "title": "Spaces of curves with constrained curvature on hyperbolic surfaces",
  "authors": [
    "Nicolau C. Saldanha",
    "Pedro Zühlke"
  ],
  "comment": "23 pages, 3 figures",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "Let $ S $ be a hyperbolic surface. We investigate the topology of the space of all curves on $ S $ which start and end at given points in given directions, and whose curvatures are constrained to lie in a given interval $ (\\kappa_1,\\kappa_2) $. These spaces fall into four qualitatively distinct classes, according to whether $ (\\kappa_1,\\kappa_2) $ contains, overlaps, is disjoint from, or contained in the interval $ [-1,1] $. Their homotopy type is computed in the latter two cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-28T13:25:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58D10",
      "53C42",
      "53A35"
    ],
    "keywords": [
      "hyperbolic surface",
      "constrained curvature",
      "spaces fall",
      "qualitatively distinct classes",
      "homotopy type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}