Geometry of $\ast$-$k$-Ricci-Yamabe soliton and gradient $\ast$-$k$-Ricci-Yamabe soliton on Kenmotsu manifolds

Abstract

The goal of the current paper is to characterize $*$-$k$-Ricci-Yamabe soliton within the framework on Kenmotsu manifolds. Here, we have shown the nature of the soliton and find the scalar curvature when the manifold admitting $*$-$k$-Ricci-Yamabe soliton on Kenmotsu manifold. Next, we have evolved the characterization of the vector field when the manifold satisfies $*$-$k$-Ricci-Yamabe soliton. Also we have embellished some applications of vector field as torse-forming in terms of $*$-$k$-Ricci-Yamabe soliton on Kenmotsu manifold. Then, we have studied gradient $\ast$-$\eta$-Einstein soliton to yield the nature of Riemannian curvature tensor. We have developed an example of $*$-$k$-Ricci-Yamabe soliton on 5-dimensional Kenmotsu manifold to prove our findings.

Pseudosymmetric normal paracontact metric space forms admitting (α, β)− type almost η−Ricci-Yamabe solitons

“…A soliton to the Ricci-Yamabe flow is called a Ricci-Yamabe soliton if it moves only by one parameter group of diffeomorphism and scaling. To be precise, a Ricci-Yamabe soliton on a Riemannian manifold (Φ, g) in [4] is a data set (g, V, λ, α, β) satisfying…”

Curvature properties of α-cosymplectic manifolds with ∗-η-Ricci-Yamabe solitons

“…Next, the notion of * -η-RYS was studied by many authors on different odd dimensional Riemannian manifolds. It should be noted that the geometry of * -k-RYS and gradient * -k-RYS on Kenmotsu manifolds were given by S. Dey and S. Roy in [4].…”