Geometry of statistical submanifolds of statistical warped product manifolds by optimization techniques

TL;DR

This paper applies optimization techniques to study the geometry of statistical submanifolds within warped product manifolds, deriving optimal inequalities that deepen understanding of their geometric properties.

Contribution

It introduces a novel approach by formulating geometric inequalities as optimization problems for statistical submanifolds in warped product manifolds.

Findings

Derived optimal Casorati inequalities

Established Chen-Ricci inequality for specific submanifolds

Extended geometric inequality framework to statistical warped product manifolds

Abstract

This paper deals with the applications of an optimization method on submanifolds, that is, geometric inequalities can be considered as optimization problems. In this regard, we obtain optimal Casorati inequalities and Chen-Ricci inequality for a statistical submanifold in a statistical warped product manifold of type $\mathbb{R} \times_{\mathfrak{f}} \overline{M}$ (almost Kenmotsu statistical manifold), where $\mathbb{R}$ and $\overline{M}$ are trivial statistical manifold and almost Kaehler statistical manifold, respectively.