{
  "id": "0704.3251",
  "version": "v2",
  "published": "2007-04-24T17:38:58.000Z",
  "updated": "2007-05-24T23:13:08.000Z",
  "title": "Equifocality of a singular riemannian foliation",
  "authors": [
    "Marcos M. Alexandrino",
    "Dirk Toeben"
  ],
  "comment": "10 pages. This version contains some misprints corrections and improvements of Corollary 1.6",
  "journal": "Proceedings of the American Mathematical Society Proc. Amer. Math. Soc. (136) (2008), 3271-3280",
  "categories": [
    "math.DG"
  ],
  "abstract": "A singular foliation on a complete riemannian manifold M is said to be riemannian if each geodesic that is perpendicular at one point to a leaf remains perpendicular to every leaf it meets. We prove that the regular leaves are equifocal, i.e., the end point map of a normal foliated vector field has constant rank. This implies that we can reconstruct the singular foliation by taking all parallel submanifolds of a regular leaf with trivial holonomy. In addition, the end point map of a normal foliated vector field on a leaf with trivial holonomy is a covering map. These results generalize previous results of the authors on singular riemannian foliations with sections.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-05-24T23:13:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C12",
      "57R30"
    ],
    "keywords": [
      "singular riemannian foliation",
      "normal foliated vector field",
      "end point map",
      "equifocality",
      "singular foliation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.3251A"
    }
  }
}