Riemannian 3-manifolds and Ricci–Yamabe solitons

Abstract

In this paper, we characterize three-dimensional Riemannian manifolds [Formula: see text] admitting Ricci–Yamabe solitons (RYSs). It is proved that if an [Formula: see text] endowed with a semi-symmetric metric [Formula: see text]-connection admits an RYS, then the scalar curvature of [Formula: see text] satisfies the Poisson equation [Formula: see text] where [Formula: see text] and [Formula: see text] We also discuss the existence of gradient RYS in Riemannian setting. Finally, we construct a nontrivial example of three-dimensional Riemannian 3-manifolds admitting RYS to prove some of our results.