On gradient Yamabe solitons conformal to a pseudo-Euclidian space

Abstract

We consider gradient Yamabe solitons, conformal to an n -dimensional pseudo-Euclidean space. We characterize all such solitons which are invariant under the action of an ( n − 1 ) -dimensional translation group and we obtain the steady solitons. Applications provide an explicit example of a complete steady gradient Yamabe soliton, conformal to the Lorentzian space.