Rigidez e inexistência de hipersuperfícies completas tipo espaço no steady state space.

In this work, we study and prove some theorems on the rigidity and nonexistence of complete spacelike hypersurfaces immersed in the Steady State Space H n+1. Such space turns out to be an open region of the De Sitter Lorentz manifold Sn+1 1 that is immersed in the Lorentz-Minkowzki space Ln+2. To ac...

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Detalhes bibliográficos
Autor: Acosta, Sergio Manuel González
Formato: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2020
País:Brasil
Recursos:Universidade Federal do Ceará (UFC)
Repositorio:Repositório Institucional da Universidade Federal do Ceará (UFC)
Idioma:portugués
OAI Identifier:oai:repositorio.ufc.br:riufc/50589
Acesso em linha:http://www.repositorio.ufc.br/handle/riufc/50589
Access Level:acceso abierto
Palavra-chave:Steady State Space
Hipersuperfícies tipo-espaço
Hiperplanos tipo-espaço
Curvaturas médias de ordem superior
Spacelike hypersurfaces
Spacelike hyperplanes
Higher order mean curvatures
Descrição
Resumo:In this work, we study and prove some theorems on the rigidity and nonexistence of complete spacelike hypersurfaces immersed in the Steady State Space H n+1. Such space turns out to be an open region of the De Sitter Lorentz manifold Sn+1 1 that is immersed in the Lorentz-Minkowzki space Ln+2. To accomplish our objective, we use a suitable extension of the Omori-Yau’s generalized maximum principle, due to Alías, Impera and Rigoli in (ALÍAS et al., 2012). The assumed geometric conditions on the behavior of the higher order mean curvatures of these complete spacelike hypersurfaces are going to give us rigidity, so that, they will be hyperplanes of H n+1. The nonexistence will be a consequence of some of the rigidity results.