Sobre rigidez de hipersuperfÃcies completas / On rigidity of complete hypersurfaces

AUTOR(ES)
FONTE

IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia

DATA DE PUBLICAÇÃO

12/08/2011

RESUMO

The purpose of this thesis is to obtain characterization theorems of complete spacelike hypersurfaces isometrically immersed in a semi-Riemannian ambient space under some restrictions on the Gauss mapping or about the r-mean curvatures of these objects. We start our work by providing necessary conditions to ensure the umbilicity of immersed hypersurfaces in the hyperbolic space Hn+1 with prescribed Gauss mapping. Next, we obtain some uniqueness results of complete hypersurfaces with bounded higher order mean curvatures in a space ER x et Mn where we suppose an appropriate condition on the normal angle of the hypersurface. In the last part of this work, we obtain Bernstein-type results concerning to complete vertical graphs with constant mean curvature immersed in a Riemannian warped product I x f Mn, where we suppose a well know convergence condition on the sectional curvature of the fibre Mn.

ASSUNTO(S)

geometria diferencial espaÃo hiperbÃlico aplicaÃÃo de gauss produto warped Ãngulo normal hyperbolic space gauss mapping warped product normal angle hipersuperfÃcies hypersurfaces

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