Conformal η-Ricci Solitons on Riemannian Submersions under Canonical Variation

Abstract

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