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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| 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 |
| 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. |
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