Variedades de Einstein e Ricci solitons com estrutura de produto torcido

In this thesis, primarily, we studied warped products semi-Riemannian Einstein manifolds. We considered the case in that the base is conformal to an n-dimensional pseudo- Euclidean space and invariant under the action of an (n 1)-dimensional translation group. We constructed new examples of Einstein...

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Detalhes bibliográficos
Autor: Sousa, Márcio Lemes de
Formato: tesis doctoral
Estado:Versión publicada
Fecha de publicación:2015
País:Brasil
Recursos:Universidade Federal de Goiás (UFG)
Repositorio:Repositório Institucional da UFG
Idioma:portugués
OAI Identifier:oai:repositorio.bc.ufg.br:tede/4958
Acesso em linha:http://repositorio.bc.ufg.br/tede/handle/tede/4958
Access Level:acceso abierto
Palavra-chave:Produto torcido
Variedades de Einstein
Ricci soliton gradiente
Warped product
Einstein manifolds
Gradient ricci soliton
CIENCIAS EXATAS E DA TERRA::MATEMATICA
Descrição
Resumo:In this thesis, primarily, we studied warped products semi-Riemannian Einstein manifolds. We considered the case in that the base is conformal to an n-dimensional pseudo- Euclidean space and invariant under the action of an (n 1)-dimensional translation group. We constructed new examples of Einstein warped products with zero Ricci curvature when the fiber is Ricci-flat. In particular, we obtain explicit solutions, in the case vacuum, for Einstein field equation. Furthermore, we consider M = B f F warped product gradient Ricci solitons. We proved that the potential function depends only on the base and the fiber F is necessarily Einstein manifold. We provide all such solutions in the case of steady gradient Ricci solitons when the base is conformal to an n-dimensional pseudo-Euclidean space, invariant under the action of an (n1)-dimensional translation group, and the fiber F is Ricci-flat.