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April 1, 2026Open Access

Golden-like Statistical Manifold Equipped with Quarter-Symmetric Metric Connection

Key Points

The aim is to explore the relationships between intrinsic and extrinsic curvatures in a GLSM with a QSMC.
Analyzed curvature inequalities in a golden-like statistical manifold.
Investigated the relationships between intrinsic and extrinsic curvatures.
Extended known inequalities using a quarter-symmetric metric connection.
Identified new geometric constraints arising from the interplay between golden-like structure and QSMC.
Suggested implications for optimization based on the extended inequalities.

Abstract

In this paper, we study curvature inequalities on a GLSM when the ambient space is equipped with a QSMC. Our focus is on the relationships between intrinsic and extrinsic curvatures arising in information geometry. The interplay between the golden-like structure and QSMC yields additional geometric constraints, extending known inequalities for statistical manifolds and suggesting consequences for optimization.

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