Abstract
In this paper, we study Riemannian maps whose total manifolds admit a Ricci soliton and give a non-trivial example of such Riemannian maps. We obtain necessary conditions for any fiber of such Riemannian map to be Ricci soliton, almost Ricci soliton and Einstein. We also obtain necessary conditions for the range space of such Riemannian map to be Ricci soliton and Einstein. Further, we calculate scalar curvature of total manifold and also for any fiber and range space. Moreover, we study the harmonicity and biharmonicity of Riemannian map from Ricci soliton and obtain necessary and sufficient conditions for such a Riemannian map to be harmonic and biharmonic.
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