Sobre a aplicação de Gauss de hipersuperficies com curvatura escalar constante em esferas

The purpose of the dissertation is to characterize hypersurfaces in the Euclidean sphere with constant mean curvature of higher order. We prove that if M is a Riemannian manifold of dimension n and the image of the Gaussian map of M is contained in a closed hemisphere of the sphere of dimension n+1...

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Detalles Bibliográficos
Autor: Macedo, Elivaldo Rodrigues
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2006
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/61259
Acceso en línea:http://www.repositorio.ufc.br/handle/riufc/61259
Access Level:acceso abierto
Palabra clave:Geometria diferencial
Hipersuperfícies
Curvatura
Aplicação de Gauss
Descripción
Sumario:The purpose of the dissertation is to characterize hypersurfaces in the Euclidean sphere with constant mean curvature of higher order. We prove that if M is a Riemannian manifold of dimension n and the image of the Gaussian map of M is contained in a closed hemisphere of the sphere of dimension n+1 then M is totally umbilical.