A Classification of Kenmotsu Manifold Admitting ⁎-Einstein Soliton

Abstract

In this paper, we initiate the study of ∗-Einstein soliton on Kenmotsu
manifold, whose potential vector field is torse-forming. Here, we have shown the
nature of the soliton and find the scalar curvature when the manifold admitting ∗-Einstein soliton on Kenmotsu manifold. Next, we have evolved the characterization of the vector field when the manifold satisfies ∗-Einstein soliton. We have embellished some applications of vector field as torse-forming in terms of ∗-Einstein soliton on Kenmotsu manifold. Also, we have studied infinitesimal CL-transformation and Schouten-Van Kampen connection on Kenmotsu manifold, whose metric is ∗-Einstein soliton. We have developed an example of ∗-Einstein soliton on 3-dimensional Kenmotsu manifold to prove our findings.

Key words and phrases. ∗-Einstein soliton, torse forming vector field, conformal Killing vector field, Kenmotsu manifold.

2010 Mathematics Subject Classification. 53C15, 53C25, 53C44.