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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2000.tde-20210729-123306
Document
Author
Full name
Armando Caputi
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2000
Supervisor
Title in Portuguese
Hipersuperfícies de co-homogeneidade 1 do espaço hiperbólico
Keywords in Portuguese
Espaços Hiperbólicos
Geometria Diferencial
Abstract in Portuguese
Em [PoSp], foi aprovado que uma hipersuperfície compacta de dimensão n > OU = 4 do espaço euclidiano, sobre a qual age um grupo compacto de isometrias com co-homogeneidade 1 e órbitas principais umbílicas, é uma hipersuperfície de revolução. Em [Se], a hipótese de compacidade da variedade foi enfraquecida: o resultado anterior foi estendido a hipersuperfícies completas com um certo controle sobre a planaridade (introduziu-se o conceito de 'não-planaridade no infinito'). No nosso trabalho, estendemos o resultado de [Se] a hipersuperfícies do espaço hiperbólico, obtendo um teorema similar com alguns exemplos a mais (cf. Teorema 3.9)
Title in English
not available
Abstract in English
Let 'M. SUP n' be a cohomogeneity one Riemannian manifold and let f : 'M. SUP n' 'seta'R. SUP n+1' be an isometric immersion. In [PoSp], for M compact and n '> OR =' 4, it was proved that if the principal orbits are umbilical in M, then f is a hypersurface of revolution. In [Se] this result was extended for complete hyperdurfaces with dimension n '> OR =' 3, assuming further a reasonable hypothesis on the flat portion of the manifold M (namely, the hypothesis of 'non-flatness at infinity'). Our purpose is to extend the above theorems for hypersurfaces of the hyperbolic space. We prove a similar result of [Se], obtaining also a class of non-rotational examples (see theorem 3.9)
 
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Publishing Date
2021-07-29
 
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