arXiv subjects
Publications and source records attributed to Márcio Lemes de Sousa.
We study Einstein riemannian manifolds endowed with a warped product structure. We focus on the case in which both the base and the fiber are Einstein manifolds and establish necessary and sufficient conditions for the warped product itself to be an Einstein manifold. Moreover, we explicitly determine the warping function when the base is the hyperbolic space.
In this paper we consider a class of Einstein warped product semi-Riemannian manifolds $\widehat{M} = M^{n}\times_{f}N^{m}$ with $n\geq 3$ and $m\geq 2$. For $\widehat{M}$ with compact base and Ricci-flat fiber, we prove that $\widehat{M}$ is simply a Riemannian product space. Then, when the base $M$ is conformal to a pseudo-Euclidean space which is invariant under the action of a $(n-1)$-dimensional translation group, we classify all such spaces. Furthermore, we get new examples of complete Einstein warped products Riemannian manifolds.
In this paper we consider $M = B\times_{f}F$ 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.