skip to main content

Equifocality of a singular Riemannian foliation

Alexandrino, Marcos M.; Toeben, Dirk Universidade De São Paulo

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, v.136, n.9, p.3271-3280, 2008

AMER MATHEMATICAL SOC 2008

Acesso online

  • Título:
    Equifocality of a singular Riemannian foliation
  • Autor: Alexandrino, Marcos M.; Toeben, Dirk
  • Universidade De São Paulo
  • Assuntos: Singular Riemannian Foliations; Equifocal Submanifolds; Isometric Actions; Manifolds; Sections; Spaces; Mathematics; Applied; Mathematics
  • É parte de: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, v.136, n.9, p.3271-3280, 2008
  • Descrição: A singular foliation on a complete Riemannian manifold M is said to be Riemannian if each geodesic that is perpendicular to a leaf at one point 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.
  • DOI: 10.1090/S0002-9939-08-09407-0
  • Títulos relacionados: Proceedings of the American Mathematical Society
  • Editor: AMER MATHEMATICAL SOC
  • Data de publicação: 2008
  • Idioma: Inglês

Buscando em bases de dados remotas. Favor aguardar.