  In this paper, we study Riemannian maps whose base manifolds admit a Ricci
soliton and give a non-trivial example of such a Riemannian map. First, we find
Riemannian curvature tensor for the base manifolds of Riemannian map $F$.
Further, we obtain the Ricci tensor and calculate the scalar curvature of the
base manifold. Moreover, we obtain necessary conditions for the leaves of
$rangeF_\ast$ to be Ricci soliton, almost Ricci soliton, and Einstein. We also
obtain necessary conditions for the leaves of $(rangeF_\ast)^\bot$ to be Ricci
soliton and Einstein. Also, we calculate the scalar curvatures of $rangeF_\ast$
and $(rangeF_\ast)^\bot$ by using Ricci soliton. Finally, we study the
harmonicity and biharmonicity of such a Riemannian map. We obtain a necessary
and sufficient condition for such a Riemannian map between Riemannian manifolds
to be harmonic. We also obtain necessary and sufficient conditions for a
Riemannian map from a Riemannian manifold to a space form that admits Ricci
soliton to be harmonic and biharmonic.
