\phi-Sectional curvature of statistical structures on almost contact metric manifolds

TL;DR

This paper investigates the ta-sectional curvature in almost contact metric manifolds with statistical structures, showing it is always non-positive and providing conditions for its vanishing and cosymplectic classification.

Contribution

It introduces the concept of ta-sectional curvature in this context and establishes new criteria for its behavior and classification of the manifold.

Findings

ta-sectional curvature is always non-positive

Conditions for ta-sectional curvature to vanish

A sufficient condition for cosymplectic statistical manifolds

Abstract

In this article, we study and analyze the \phi-sectional curvature induced by a statistical structure on an almost contact metric manifold. We demonstrate that this sectional curvature is always non-positive. Additionally, we present equivalent statements regarding the vanishing of this type of sectional curvature. Furthermore, we derive a sufficient condition for an almost contact statistical manifold to be classified as a cosymplectic statistical manifold.