Abstract
This research article endeavors to discuss the attributes of Riemannian submersions under the canonical variation in terms of the conformal eta-Ricci soliton and gradient conformal eta-Ricci soliton with a potential vector field zeta. Additionally, we estimate the various conditions for which the target manifold of Riemannian submersion under the canonical variation is a conformal eta-Ricci soliton with a Killing vector field and a phi(Ric)-vector field. Moreover, we deduce the generalized Liouville equation for Riemannian submersion under the canonical variation satisfying by a last multiplier psi of the vertical potential vector field zeta and show that the base manifold of Riemanian submersion under canonical variation is an eta Einstein for gradient conformal eta-Ricci soliton with a scalar concircular field gamma on base manifold. Finally, we illustrate an example of Riemannian submersions between Riemannian manifolds, which verify our results.