Variedades de Einstein e Ricci solitons com estrutura de produto torcido
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2015-07-03
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Universidade Federal de Goiás
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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SOUSA, Márcio Lemes de. Variedades de Einstein e Ricci solitons com estrutura de produto torcido. 2015. 63 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2015.