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

Authors : Santu DEY, Pişcoran Laurianioan LAURİANIOAN, Soumendu ROY

Pages : 907-922

Doi:10.15672/hujms.1074722

View : 299 | Download : 438

Publication Date : 2023-08-15

Article Type : Research Paper

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