{
  "id": "math/0509405",
  "version": "v1",
  "published": "2005-09-18T18:21:55.000Z",
  "updated": "2005-09-18T18:21:55.000Z",
  "title": "Proofs of Conjectures about singular riemannian foliations",
  "authors": [
    "Marcos M. Alexandrino"
  ],
  "comment": "Latex2e; The final publication is available at springerlink.com http://www.springerlink.com/content/q48682633730t831/",
  "journal": "Geom. Dedicata 119(2006) No1, 219-234",
  "doi": "10.1007/s10711-006-9073-0",
  "categories": [
    "math.DG",
    "math.GT"
  ],
  "abstract": "We prove that if the normal distribution of a singular riemannian foliation is integrable, then each leaf of this normal distribution can be extended to be a complete immersed totally geodesic submanifold (called section) which meets every leaf orthogonally. In addition the set of regular points is open and dense in each section. This result generalizes a result of Boualem and solves a problem inspired by a remark of Palais and Terng and a work of Szenthe about polar actions. We also study the singular holonomy of a singular riemannian foliation with sections (s.r.f.s for short) and in particular the transverse orbit of the closure of each leaf. Furthermore we prove that the closure of the leaves of a s.r.f.s. on M form a partition of M which is a singular riemannian foliation. This result proves partially a conjecture of Molino.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-09-18T18:21:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C12",
      "57R30"
    ],
    "keywords": [
      "singular riemannian foliation",
      "conjecture",
      "normal distribution",
      "complete immersed totally geodesic submanifold",
      "result generalizes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9405A"
    }
  }
}