Geometry of almost contact metrics as a ∗-conformal Ricci–Yamabe solitons and related results

Abstract

The goal of this paper is to study certain types of metric such as ∗-conformal Ricci–Yamabe soliton (RYS), whose potential vector field is torse-forming on Kenmotsu manifold. Here, we establish the conditions for solitons to be expanding, shrinking or steady and find the scalar curvature when the manifold admits ∗-conformal RYS on Kenmotsu manifold. Next, we developed the nature of the vector field when the manifold satisfies ∗-conformal RYS. Also, we have adorned some applications of torse-forming vector field in terms of ∗-conformal RYS on Kenmotsu manifold. We have also studied infinitesimal CL-transformation and Schouten–van Kampen connection on Kenmotsu manifold, whose metric is ∗-conformal RYS. We present an example of ∗-conformal RYS on three-dimensional Kenmotsu manifold, and verify some of our findings.