A study of conformal Riemannian maps whose total manifold admits a Yamabe soliton

Abstract

We study conformal Riemannian maps between Riemannian manifolds and derive expression of scalar curvature for its total manifold. Later, we study conformal Riemannian maps whose total manifold admits a Yamabe soliton and obtain conditions for fiber and range space of such maps to be Yamabe soliton. We also present a characterization theorem for a Yamabe soliton to be an almost Yamabe soliton for conformal Riemannian maps. Finally, we derive a nontrivial example of a conformal Riemannian map whose total manifold admits a Yamabe soliton.