{
  "id": "1704.04704",
  "version": "v1",
  "published": "2017-04-16T00:31:01.000Z",
  "updated": "2017-04-16T00:31:01.000Z",
  "title": "Algebraic characterizations of sub-Riemannian geodesics in semi-simple, connected, compact Lie groups",
  "authors": [
    "András Domokos",
    "Matthew Krauel",
    "Vincent Pigno",
    "Corey Shanbrom",
    "Michael VanValkenburgh"
  ],
  "comment": "20 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper we will use the algebraic information encoded in the root system of a semi-simple, connected, compact Lie group to describe properties of sub-Riemannian geodesics. First we give an algebraic proof that all sub-Riemannian geodesics are normal. We then find characterizations and lengths of the Riemannian and sub-Riemannian geodesic loops in simple, simply connected, compact Lie groups. We provide specific calculations for $SU (2)$ and $SU (3)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-16T00:31:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C17",
      "53C22",
      "22E30",
      "51N30"
    ],
    "keywords": [
      "compact lie group",
      "algebraic characterizations",
      "semi-simple",
      "sub-riemannian geodesic loops",
      "algebraic information"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}