Solitonic aspects of submanifolds in Kenmotsu statistical manifolds

TL;DR

This paper explores the properties of statistical solitons, Yamabe solitons, and curvature in Kenmotsu statistical manifolds, including submanifolds with concircular and concurrent vector fields, providing new examples and theoretical insights.

Contribution

It introduces the study of statistical solitons and Yamabe solitons on Kenmotsu statistical manifolds and their submanifolds, with new examples and curvature analysis.

Findings

Existence of statistical solitons and Yamabe solitons on Kenmotsu statistical manifolds.

Characterization of curvature properties related to these solitons.

Construction of explicit 5-dimensional examples supporting the theoretical results.

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.