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Polar foliations and isoparametric maps

Alexandrino, Marcos M. Universidade De São Paulo

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, DORDRECHT, v. 41, n. 2, pp. 187-198, FEB, 2012

SPRINGER; DORDRECHT 2012-02

Acesso online

  • Título:
    Polar foliations and isoparametric maps
  • Autor: Alexandrino, Marcos M.
  • Universidade De São Paulo
  • Assuntos: Singular Riemannian Foliations; Polar Actions; Polar Foliations; Isoparametric Maps; Transnormal Maps; Singular Riemannian Foliations; Manifolds; Sections; Mathematics
  • É parte de: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, DORDRECHT, v. 41, n. 2, pp. 187-198, FEB, 2012
  • Descrição: A singular Riemannian foliation F on a complete Riemannian manifold M is called a polar foliation if, for each regular point p, there is an immersed submanifold Sigma, called section, that passes through p and that meets all the leaves and always perpendicularly. A typical example of a polar foliation is the partition of M into the orbits of a polar action, i.e., an isometric action with sections. In this article we prove that the leaves of H : M -> Sigma, coincide with the level sets of a smooth map H: M -> Sigma, if M is simply connected. In particular, the orbits of a polar action on a simply connected space are level sets of an isoparametric map. This result extends previous results due to the author and Gorodski, Heintze, Liu and Olmos, Carter and West, and Terng.
    CNPq (Conselho Nacional de Desenvolvimento Cientifico e TecnologicoBrazil)
    CNPq-Conselho Nacional de Desenvolvimento Cientifico e Tecnologico-Brazil
    FAPESP
  • DOI: 10.1007/s10455-011-9277-x
  • Títulos relacionados: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY
  • Editor: SPRINGER; DORDRECHT
  • Data de publicação: 2012-02
  • Idioma: Inglês

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