{
  "id": "2202.09085",
  "version": "v1",
  "published": "2022-02-18T09:04:37.000Z",
  "updated": "2022-02-18T09:04:37.000Z",
  "title": "Homogeneous geodesics in sub-Riemannian geometry",
  "authors": [
    "A. V. Podobryaev"
  ],
  "categories": [
    "math.DG",
    "math.OC"
  ],
  "abstract": "We study homogeneous geodesics of sub-Riemannian manifolds, i.e., normal geodesics that are orbits of one-parametric subgroups of isometries. We obtain a criterion for a geodesic to be homogeneous in terms of its initial momentum. We prove that any weakly commutative sub-Riemannian homogeneous space is geodesic orbit, that means all geodesics are homogeneous. We discuss some examples of geodesic orbit sub-Riemannian manifolds. In particular, we show that geodesic orbit Carnot groups are only groups of step $1$ and $2$. Finally, we get a broad condition for existence of at least one homogeneous geodesic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-18T09:04:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C30",
      "53C17",
      "35R03"
    ],
    "keywords": [
      "homogeneous geodesic",
      "sub-riemannian geometry",
      "geodesic orbit carnot groups",
      "geodesic orbit sub-riemannian manifolds",
      "weakly commutative sub-riemannian homogeneous space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}