REDUCTION OF GRADIENT RICCI SOLITON EQUATION

We consider gradient Ricci solitons conformal to an n-dimensional pseudo-Euclidean space and we describe entirely the most general substitution that reduces the resulting system of partial differential equations, originated from the gradient Ricci soliton equations, to a system of ordinary differential equations. As a consequence, the gradient Ricci solitons that arise from the reduced system are invariant under the action of either an (n - 1)-dimensional translation group or the pseudo-orthogonal group acting on the corresponding n-dimensional pseudo-Euclidean space. The reduced system of ordinary differential equations is given. From such a system, particular solutions are obtained.