{
  "id": "0808.4059",
  "version": "v2",
  "published": "2008-08-29T09:59:21.000Z",
  "updated": "2008-09-25T10:51:08.000Z",
  "title": "Any sub-Riemannian Metric has Points of Smoothness",
  "authors": [
    "Andrei Agrachev"
  ],
  "categories": [
    "math.DG",
    "math.OC"
  ],
  "abstract": "We prove the result stated in the title; it is equivalent to the existence of a regular point of the sub-Riemannian exponential mapping. We also prove that the metric is analytic on an open everywhere dense subset in the case of a complete real-analytic sub-Riemannian manifold.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-09-25T10:51:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sub-riemannian metric",
      "smoothness",
      "complete real-analytic sub-riemannian manifold",
      "sub-riemannian exponential",
      "regular point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.4059A"
    }
  }
}