{
  "id": "math/0411415",
  "version": "v1",
  "published": "2004-11-18T19:50:18.000Z",
  "updated": "2004-11-18T19:50:18.000Z",
  "title": "Singular riemannian foliations on simply connected spaces",
  "authors": [
    "Marcos M. Alexandrino",
    "Dirk Toeben"
  ],
  "comment": "17 pages, Latex 2e",
  "journal": "Differential Geom. and Appl. 24 (2006) 383-397",
  "categories": [
    "math.DG",
    "math.GT"
  ],
  "abstract": "A singular riemannian foliation on a complete riemannian manifold is said to be riemannian if each geodesic that is perpendicular at one point to a leaf remains perpendicular to every leaf it meets. The singular foliation is said to admit sections if each regular point is contained in a totally geodesic complete immersed submanifold that meets every leaf orthogonally and whose dimension is the codimension of the regular leaves. A typical example of such singular foliation is the partition by orbits of a polar action,e.g. the orbits of the adjoint action of a compact Lie group on itself. We prove that a singular riemannian foliation with compact leaves that admit sections on a simply connected space has no exceptional leaves, i.e., each regular leaf has trivial normal holonomy. We also prove that there exists a convex fundamental domain in each section of the foliation and in particular that the space of leaves is a convex Coxeter orbifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-11-18T19:50:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C12",
      "57R30"
    ],
    "keywords": [
      "singular riemannian foliation",
      "simply connected space",
      "geodesic complete immersed submanifold",
      "singular foliation",
      "admit sections"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....11415A"
    }
  }
}