Clairaut conformal submersions from Ricci solitons

In this study, we investigate Clairaut conformal submersions in the context of total manifolds that support a Ricci soliton structure. We begin by deriving the scalar curvature and Ricci tensor expressions associated with these manifolds, and we establish criteria under which the fibres can be characterized as almost Ricci solitons or Einstein manifolds. Additionally, we identify the conditions required for the base manifold to admit Ricci soliton and Einstein structures. We also determine the necessary conditions for a vector field ζ to be conformal or Killing. Moreover, we demonstrate that when the potential vector field of the Ricci soliton is the mean curvature vector field H of Kerϑ∗, the total manifold satisfies the properties of a gradient Ricci soliton. Finally, by solving a corresponding Poisson equation, we derive a necessary and sufficient condition for these submersions to be harmonic.