August 23, 2025Open Access

Curvature Inequalities in Golden-like Statistical Manifolds Admitting Semi-Symmetric Metric Connection

Key Points

Curvature inequalities in golden-like statistical manifolds reveal new geometric insights and extend known results.
The study establishes that these properties relate closely to classical information geometry principles.
Assessment involved examining the semi-symmetric metric connection's impact on geometric properties.
These findings may enable advances in optimization strategies and theoretical understanding of divergence in statistical contexts.

Abstract

This article investigates fundamental inequalities within a golden-like statistical manifold (GLSM) equipped with a semi-symmetric metric connection (SSMC). We explore key geometric and analytical properties, including curvature relations and inequalities analogous to those in classical information geometry. The interplay between the golden-like structure and the SSMC yields new insights into the underlying differential geometric framework. Our results extend known inequalities in the statistical manifold (SM), providing a foundation for further studies in optimization and divergence theory within this generalized framework.

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