Hipersuperficies de coomogeneidade um na esfera euclidiana

AUTOR(ES)

Jose Carlos Almeida de Lima

DATA DE PUBLICAÇÃO

2002

RESUMO

In 1994, Podestà and Spiro proved that a compact hypersurface of cohomogeneity one, f : Mn + IRn+1, n _ 4, whose principal orbits are umbilical in M is a hyper surface ofrevolution. In 1996, in his Ph.D. thesis, Seixas weakened the hypothesis of this theorem, proving the result for complete hypersurfaces and extended the result of Podestà and Spiro to the cases of complete manifolds with some restrictions on the flat part of M. Besides this, Seixas considered the tridimensional case, obtaining an extension of the theorem in this case. Following Seixas, Caputi, in 2000, in his Ph.D thesis, extended the result of Seixas for complete hypersurfaces with the dimension greater than or equal to 4 in the hyperbolic space. Our work consists of considering this problem on the Euclidean sphere. Just like in the work of Seixas, we prove that a complete hypersurface, f : Mn__ sn+l, n _ 4, on which a compact group of isometries acts with cohomogeneity one and whose principal orbits are umbilical in M is a hypersurface of revolution

ASSUNTO(S)

lie geometria diferencial imersões (matematica) grupos de

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