Conformal Ricci-Yamabe Solitons on Warped Product Manifolds

Abstract

Self similar solutions of the conformal Ricci-Yamabe flow equation is called conformal Ricci-Yamabe solitons. This paper is mainly concern with the study of conformal Ricci-Yamabe solitons within the structure of warped product manifolds which extends the notion of usual Riemannian product manifolds. First, The base and the fiber share the same property is prove that when a warped product manifold admits conformal Ricci-Yamabe soliton. In the next section warped product manifolds is used to study the characterization of conformal Ricci-Yamabe solitons in terms of Killing and conformal vector fields. Next, we prove that a conformal Ricci-Yamabe soliton with concurrent potential vector field admitted on a warped product manifold is Ricci flat.