Variedades de Einstein e Ricci solitons com estrutura de produto torcido

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Bibliographic Details
Main Author:	Sousa, Márcio Lemes de
Publication Date:	2015
Format:	Doctoral thesis
Language:	por
Source:	Repositório Institucional da UFG
Download full:	http://repositorio.bc.ufg.br/tede/handle/tede/4958
Summary:	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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