On conformal Riemannian maps whose total manifold admits a Ricci soliton

Abstract

We study conformal Riemannian maps between the Riemannian manifolds. We derive a Bochner type identity and conditions for such maps to be harmonic. Later, we study conformal Riemannian maps whose total manifold admits a Ricci soliton and present a non-trivial example of such conformal Riemannian maps. We also obtain conditions for fiber and range space of such maps to be Ricci soliton and Einstein. We derive conditions for conformal Riemannian maps whose total manifold admits a Ricci soliton to be harmonic and biharmonic.