Optimization Methods to Statistical Submanifolds in Statistical Warped Product Manifolds

Abstract

This research paper strives to address the utilization of an optimization technique on submanifolds. Specifically, it explores the concept of treating geometric inequalities as optimization challenges. Within this framework, the paper examines two categories of inequalities: the optimal Casorati inequalities and the Chen-Ricci inequality. These inequalities are investigated in the context of a statistical submanifold situated within an almost Kenmotsu statistical manifold. Notably, this manifold represents a statistical warped product of a trivial statistical manifold and an almost K\"ahler statistical manifold.