{
  "id": "1502.06018",
  "version": "v1",
  "published": "2015-02-20T21:44:09.000Z",
  "updated": "2015-02-20T21:44:09.000Z",
  "title": "Riemannian and Sub-Riemannian geodesic flows",
  "authors": [
    "Mauricio Godoy Molina",
    "Erlend Grong"
  ],
  "comment": "12 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "In the present paper we show that the geodesic flows of a sub-Riemannian metric and that of a Riemannian extension commute if and only if the extended metric is parallel with respect to a certain connection. This helps us to describe the geodesic flow of sub-Riemannian metrics on totally geodesic Riemannian submersions. As a consequence we can characterize sub-Riemannian geodesics as the horizontal lifts of projections of Riemannian geodesics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-20T21:44:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C17",
      "53C22",
      "53C12"
    ],
    "keywords": [
      "sub-riemannian geodesic flows",
      "sub-riemannian metric",
      "totally geodesic riemannian submersions",
      "riemannian extension commute",
      "horizontal lifts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}