Solitonic aspects of submanifolds in Kenmotsu statistical manifolds

Abstract

The differential geometry of Kenmotsu manifold is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. In fact, its statistical counterpart, that is, Kenmotsu statistical manifold also has same importance as that of Kenmotsu manifold. Theoretical physicists have also been looking into the equation of Ricci soliton and Yamabe soliton in relation with Einstein manifolds, quasi-Einstein manifolds and string theory. In this research article, first we examine the statistical solitons and Yamabe soliton on Kenmotsu statistical manifolds with some related examples. Then we investigate some statistical curvature properties of Kenmotsu statistical manifolds. Also, we study the statistical solitons on submanifolds of Kenmotsu statistical manifold with concircular vector field. Furthermore, we discuss the behavior of almost quasi-Yamabe soliton on submanifolds of Kenmotsu statistical manifolds endowed with concircular vector field and concurrent vector filed. Finally, we furnish an example of $5$-dimensional Kenmotsu statistical manifolds admitting a statistical soliton and almost quasi-Yamabe soliton as well in the support of this study.