Hacettepe Journal of Mathematics and Statistics 2651-477X 2651-477X Hacettepe University 10.15672/hujms.1074722 Mathematical Sciences Matematik Geometry of $\ast$-$k$-Ricci-Yamabe soliton and gradient $\ast$-$k$-Ricci-Yamabe soliton on Kenmotsu manifolds https://orcid.org/0000-0002-2601-3788 Dey Santu Bidhan Chandra College Asansol-4 https://orcid.org/0000-0003-2269-718X Laurian-ıoan Pişcoran Laurian-ioan Technical University of Cluj Napoca https://orcid.org/0000-0003-2236-8482 Roy Soumendu School of Advanced Sciences 08 15 2023 52 4 907 922 02 16 2022 11 20 2022 Copyright © 2002, Hacettepe Journal of Mathematics and Statistics 2002 Hacettepe Journal of Mathematics and Statistics

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.

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