{
  "id": "1312.1675",
  "version": "v4",
  "published": "2013-12-05T20:37:54.000Z",
  "updated": "2014-11-03T12:44:04.000Z",
  "title": "Components of spaces of curves with constrained curvature on flat surfaces",
  "authors": [
    "Nicolau C. Saldanha",
    "Pedro Zühlke"
  ],
  "comment": "38 pages, 11 figures. In this version, some results in section 7 which were not used elsewhere were removed to make the paper shorter and less technical. Also, the notation in section 3 has been changed slightly to make it compatible with arXiv:1410.8590",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "Let $S$ be a complete flat surface, such as the Euclidean plane. We obtain direct characterizations of the connected components 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, in terms of all parameters involved. Many topological properties of these spaces are investigated. Some conjectures of L. E. Dubins are proved.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-05-05T00:48:47.000Z",
      "title": "Spaces of curves with constrained curvature on flat surfaces, I",
      "comment": "42 pages, 12 figures. The proof of (former) lemma 3.2 was incomplete and has been rewritten. Some results in section 1 dealing with general surfaces were deleted to be incorporated into another paper. Changes to other sections were minor",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-11-03T12:44:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A04",
      "53C42",
      "57N20"
    ],
    "keywords": [
      "constrained curvature",
      "complete flat surface",
      "euclidean plane",
      "direct characterizations",
      "connected components"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.1675S"
    }
  }
}