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Conformal Submersions Whose Total Manifolds Admit a Ricci Soliton
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Journal Article
Conformal Submersions Whose Total Manifolds Admit a Ricci Soliton
2023
Overview
In this paper, we study conformal submersions from Ricci solitons to Riemannian manifolds with non-trivial examples. First, we study some properties of the O’Neill tensor
A
in the case of conformal submersion. We also find a necessary and sufficient condition for conformal submersion to be totally geodesic and calculate the Ricci tensor for the total manifold of such a map with different assumptions. Further, we consider a conformal submersion
F
:
M
→
N
from a Ricci soliton to a Riemannian manifold and obtain necessary conditions for the fibers of
F
and the base manifold
N
to be Ricci soliton, almost Ricci soliton and Einstein. Moreover, we find necessary conditions for a vector field and its horizontal lift to be conformal on
N
and
(
Ker
F
∗
)
⊥
,
respectively. Also, we calculate the scalar curvature of Ricci soliton
M
. Finally, we obtain a necessary and sufficient condition for
F
to be harmonic.
Publisher
Springer International Publishing,Springer Nature B.V
