Sobre a Geometria de Imersões Riemannianas
Our purpose is to study the geometry of Riemannian immersions in certain semi- Riemannian manifolds. Initially, considering linearWeingarten hypersurfaces immersed in locally symmetric manifolds and, imposing suitable constraints on the scalar curvature, we guarantee that such a hypersurface is eith...
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| Tipo de documento: | tese |
| Estado: | Versão publicada |
| Data de publicação: | 2015 |
| País: | Brasil |
| Recursos: | Universidade Federal da Paraíba (UFPB) |
| Repositório: | Biblioteca Digital de Teses e Dissertações da UFPB |
| Idioma: | português |
| OAI Identifier: | oai:repositorio.ufpb.br:tede/8031 |
| Acesso em linha: | https://repositorio.ufpb.br/jspui/handle/tede/8031 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Variedades localmente simétrica Locally symmetric manifolds Subvariedades Weingarten lineares Hipersuperfícies totalmente umbílicas Hipersuperfícies isoparamétricas Subvariedades tipo-espaço Steady state space Linear Weingarten submanifold Totally umbilical hypersurfaces Isoparametric hypersurfaces Spacelike submanifolds CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| Resumo: | Our purpose is to study the geometry of Riemannian immersions in certain semi- Riemannian manifolds. Initially, considering linearWeingarten hypersurfaces immersed in locally symmetric manifolds and, imposing suitable constraints on the scalar curvature, we guarantee that such a hypersurface is either totally umbilical or isometric to a isoparametric hypersurface with two distinct principal curvatures, one of them being simple. In higher codimension, we use a Simons type formula to obtain new characterizations of hyperbolic cylinders through the study of submanifolds having parallel normalized mean curvature vector field in a semi-Riemannian space form. Finally, we investigate the rigidity of complete spacelike hypersurfaces immersed in the steady state space via applications of some maximum principles. |
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