{
  "id": "2002.12293",
  "version": "v1",
  "published": "2020-02-27T18:04:12.000Z",
  "updated": "2020-02-27T18:04:12.000Z",
  "title": "Branching geodesics in sub-Riemannian geometry",
  "authors": [
    "Thomas Mietton",
    "Luca Rizzi"
  ],
  "comment": "9 pages, 1 figure",
  "categories": [
    "math.DG",
    "math.MG"
  ],
  "abstract": "In this note, we show that sub-Riemannian manifolds can contain branching normal minimizing geodesics. This phenomenon occurs if and only if a normal geodesic has a discontinuity in its rank at a non-zero time, which in particular for a strictly normal geodesic means that it contains a non-trivial abnormal subsegment. The simplest example is obtained by gluing the three-dimensional Martinet flat structure with the Heisenberg group in a suitable way. We then use this example to construct more general types of branching.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-27T18:04:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C17",
      "49J15"
    ],
    "keywords": [
      "sub-riemannian geometry",
      "branching geodesics",
      "three-dimensional martinet flat structure",
      "contain branching normal minimizing geodesics",
      "strictly normal geodesic means"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}