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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| 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 |
| 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). |
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