Study of Solitons on submanifolds of Kenmotsu statistical manifolds

The differential geometry of Kenmotsu manifold is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. 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 servey, we examine the Ricci solitons and Yamabe soliton on statistical counterpart of a Kenmotsu manifold, that is, Kenmotsu statistical manifold with some related examples. We investigate some statistical curvature properties of Kenmotsu statistical manifolds. Also, we study the almost $\eta$-Ricci solitons on submanifolds of Kenmotsu statistical manifold with concircular vector field. Furthermore, we have also discuss the behavior of almost quasi-Yamabe soliton on subamnifolds of Kenmotsu statistical manifolds endowed with concircular vector field and concurrent vector filed. Finally, we have furnish an example of $5$-dimensional Kenmotsu statistical manifolds admitting the $\eta$-Ricci soliton and almost quasi-Yamabe soliton as well.Comment: arXiv admin note: text overlap with arXiv:1902.0929