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

10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex