Conformal Ricci-Yamabe solitons on warped product manifolds

Abstract

Self-similar solutions of the conformal Ricci-Yamabe flow equation are called conformal Ricci-Yamabe solitons. This paper mainly concerned with the study of conformal Ricci-Yamabe solitons within the structure of warped product manifolds, which extend the notion of usual Riemannian product manifolds. First, the proof is provided that the base and the fiber sharing the same property implies the existence of a warped product manifold admitting a conformal Ricci-Yamabe soliton. In the next section, warped product manifolds are used to study the characterization of conformal Ricci-Yamabe solitons in terms of Killing and conformal vector fields. Finally, we prove that a conformal Ricci-Yamabe soliton with a concurrent potential vector field admitted on a warped product manifold is Ricci flat.