In this paper, we studied the geometrical aspects of a perfect fluid spacetime in terms of conformal Ricci soliton and conformal [Formula: see text]-Ricci soliton with torse-forming vector field [Formula: see text]. Condition for the conformal Ricci soliton to be steady, expanding or shrinking are also given. In particular case, when the potential vector filed [Formula: see text] of the soliton is of gradient type, we derive, from the conformal [Formula: see text]-Ricci soliton equation, a Laplacian equation.
The object of the present research is to study the (ϵ,δ)-TransSasakian manifolds addmitting the η-Ricci Solitons. It is shown that a sym-metric second order covariant tensor in an (ϵ,δ)-Trans Sasakian manifold isa constant multiple of metric tensor. Also an example of η-Ricci soliton in3-diemsional (ϵ,δ)-Trans Sasakian manifold is provided in the region where(ϵ,δ)-Trans Sasakian manifold expanding.
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.
We study statistical submersions between statistical manifolds. In particular, we establish Chen–Ricci inequalities of statistical submersions between statistical manifolds and a [Formula: see text] Chen-type inequality for statistical submersions. Some applications are also given.
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