{
  "id": "2212.07615",
  "version": "v1",
  "published": "2022-12-15T04:46:47.000Z",
  "updated": "2022-12-15T04:46:47.000Z",
  "title": "Legendre singularities of sub-Riemannian geodesics",
  "authors": [
    "Goo Ishikawa",
    "Yumiko Kitagawa"
  ],
  "comment": "2 figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $M$ be a surface with a Riemannian metric and $UM$ the unit tangent bundle over $M$ with the canonical contact sub-Riemannian structure $D$ on $UM$. In this paper, the complete local classification of singularities, under the Legendre fibration $UM$ over $M$, is given for sub-Riemannian geodesics of $(UM, D)$. Legendre singularities of sub-Riemannian geodesics are classified completely also for another Legendre fibration from $UM$ to the space of Riemannian geodesics on $M$. The duality on Legendre singularities is observed related to the pendulum motion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-15T04:46:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D25",
      "53B10",
      "49K15",
      "58K40",
      "53A20"
    ],
    "keywords": [
      "sub-riemannian geodesics",
      "legendre singularities",
      "legendre fibration",
      "unit tangent bundle",
      "canonical contact sub-riemannian structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}