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

Year 2023, , 907 - 922, 15.08.2023

Santu Dey , Pişcoran Laurian-ioan Laurian-ıoan , Soumendu Roy

https://doi.org/10.15672/hujms.1074722

Cited By: 4

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

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