Gradient Ricci Solitons with Structure of Warped Product

  title={Gradient Ricci Solitons with Structure of Warped Product},
  author={M{\'a}rcio Lemes de Sousa and Romildo Pina},
  journal={Results in Mathematics},
In this paper we consider semi-Riemannian warped product gradient Ricci solitons. We prove that the potential function depends only on the base and the fiber 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 is Ricci-flat.