Optimization of Soliton Structures Using Lifting Theory on Tangent Bundles of Statistical Kenmotsu Manifolds

This paper investigates the optimization of soliton structures on tangent bundles of statistical Kenmotsu manifolds through lifting theory. By constructing lifted statistical Kenmotsu structures using semisymmetric metric and nonmetric connections, we derive explicit expressions for the curvature tensor, Ricci operator, and scalar curvature. We analyze Ricci, η-Ricci, and Yamabe solitons in this lifted setting, classifying conditions under which the tangent bundle satisfies Einstein and quasi-Einstein properties. The corresponding soliton constants are computed, demonstrating how lifting enhances soliton characteristics. The curvature constraint Ric⋅R=0 is examined, yielding new geometric identities. A concrete 3-dimensional example validates the theory, providing explicit expanding and shrinking soliton solutions under both types of semisymmetric connections using partial differential equations. This work extends previous studies on statistical and Sasakian statistical manifolds, illustrating how lifting theory optimizes soliton structures in tangent bundles.