2015-11-302015-07-03SOUSA, 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.http://repositorio.bc.ufg.br/tede/handle/tede/4958In 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 (n􀀀1)-dimensional translation group, and the fiber F is Ricci-flat.application/pdfAcesso AbertoProduto torcidoVariedades de EinsteinRicci soliton gradienteWarped productEinstein manifoldsGradient ricci solitonCIENCIAS EXATAS E DA TERRA::MATEMATICATese