Sobre a aplicação de Gauss para hipersuperfícies de curvatura média constante na esfera

The objective of this dissertation is to show a similar result of Bernstein Theorem about minimal hypersurfaces in Euclidian space, that is, to show that that result is generalized to hypersurfaces of Sn+1 with constant mean curvature, whose Gauss image is contained in a closed hemisphere of Sn+1(Th...

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Detalles Bibliográficos
Autor: Silva, Adam Oliveira da
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2009
País:Brasil
Institución:Universidade Federal do Ceará (UFC)
Repositorio:Repositório Institucional da Universidade Federal do Ceará (UFC)
Idioma:portugués
OAI Identifier:oai:repositorio.ufc.br:riufc/61217
Acceso en línea:http://www.repositorio.ufc.br/handle/riufc/61217
Access Level:acceso abierto
Palabra clave:Geometria diferencial
Curvatura média
Aplicação de Gauss
Descripción
Sumario:The objective of this dissertation is to show a similar result of Bernstein Theorem about minimal hypersurfaces in Euclidian space, that is, to show that that result is generalized to hypersurfaces of Sn+1 with constant mean curvature, whose Gauss image is contained in a closed hemisphere of Sn+1(Theorem 3.1). However, in the case where the hypersurface is minimal, we will use in the proof of this theorem a result about the characterization of the hyperspheres of Sn+1 among all complete hypersurfaces in Sn+1 in terms of their Gauss images (Theorem 2.1).