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.

在本文中，我们研究了总流形允许 Ricci 孤子的黎曼映射，并给出了此类黎曼映射的一个重要示例。我们得到了这样的黎曼映射的任何纤维都是 Ricci 孤子，几乎是 Ricci 孤子和爱因斯坦的必要条件。我们还得到了该黎曼映射的距离空间为 Ricci 孤子和爱因斯坦的必要条件。此外，我们计算总流形以及任何纤维和距离空间的标量曲率。此外，我们从Ricci孤子研究了黎曼映射的调和性和双调和性，得到了黎曼映射调和和双调和的充要条件。