2021-03-052021-03-052021-12-05CORREIA, P. G. Variedades quasi-Einstein com simetrias e generalizações. 2021. 91 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2021.http://repositorio.bc.ufg.br/tede/handle/tede/11141In this work we study quasi-Einstein warped products and generalized quasi-Einstein manifolds locally conformally flat. We prove that in some quasi-Einstein semi-Riemannian warped product the fiber is necessarily an Einstein manifold. We provide all quasi-Einstein manifolds when r-Bakry-Émery tensor is null, the base is conformal to a n-dimensional pseudo-Euclidean space, invariant under the action of the (n-1)-dimensional translation group, the potential function depends only on the base and the fiber is Ricci-flat. As an application, we provide a family of Ricci-flat warped product whose base is not locally conformally flat. Considering generalized m-quasi-Einstein manifolds conformal to the pseudo-Euclidean space, we used an ansatz method to obtain the most general symmetry group of maximal dimension in which there are solutions to the system of equations that describe such manifolds. In addition, using the same method, we show that there is no different invariant of smaller dimension on a generalized m-quasi-Einstein manifold.Attribution-NonCommercial-NoDerivatives 4.0 InternationalProduto torcido quasi-EinsteinVariedade quasi-Einstein generalizada localmente conformemente planaVariedade de EinsteinQuasi-Einstein warped productGeneralized quasi-Einstein manifold locally conformally flatEinstein manifoldCIENCIAS EXATAS E DA TERRA::MATEMATICATese