On warped product gradient Yamabe solitons

Abstract

The purpose of this article is to study gradient Yamabe solitons on top of warped product manifolds. First we prove triviality results in the case of a bounded warping function on a noncompact base and then, for compact base. In order to provide nontrivial examples, we consider the base conformal to a semi-Euclidean space, which is invariant under the action of a translation group, and then we characterize steady solitons. We use this method to give infinitely many explicit examples of complete steady gradient Yamabe solitons.