Sobre rigidez de hipersuperfícies completas

• Autor(a) principal: Aquino, Cícero Pedro de
• Data de Publicação: 2011
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Federal do Ceará (UFC)
• Texto Completo: http://www.repositorio.ufc.br/handle/riufc/4081
• topic: Hipersuperfícies; Geometria diferencial

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.