On gradient Schouten solitons conformal to a pseudo-Euclidean space

Abstract

In this paper we consider $$\rho $$ -Einstein solitons that are conformal to a pseudo-Euclidean space and invariant under the action of the pseudo-orthogonal group. We provide all the solutions for the gradient Schouten soliton case. Moreover, we proved that if a gradient Schouten soliton is both complete, conformal to a Euclidean metric, and rotationally symmetric, then it is isometric to $${\mathbb {R}}\times {\mathbb {S}}^{n-1}$$ .