Invariant solutions for gradient Ricci almost solitons

Abstract

In this paper we provide an ansatz that reduces a pseudo-Riemannian gradient Ricci almost soliton (PDE) into an integrable system of ODE. First, considering a warped structure with conformally flat base invariant under the action of an \((n-1)\)-dimensional translation group and semi-Riemannian Einstein fiber, we provide the ODE system which characterizes all such solitons. Then, we also provide a classification for a conformally flat pseudo-Riemannian gradient Ricci almost soliton invariant by the actions of a translation group or a pseudo-orthogonal group. Finally, we conclude with some explicit examples.