Extending Information Geometry: Quasi-Statistical Structures on Metallic-Like Pseudo-Riemannian Manifolds

Year 2026, Volume: 18 Issue: 1, 248 - 266, 23.02.2026

Aydın Gezer , Olgun Durmaz , Buşra Aktaş

https://doi.org/10.47000/tjmcs.1789376

https://izlik.org/JA77LG87RB

Abstract

In this paper, we investigate the conditions under which quasi-statistical structures can be realized on metallic-like pseudo-Riemannian manifolds. By combining the flexibility of quasi-statistical geometry with the algebraic richness of metallic-like structures, we provide a unified framework for analyzing compatibility conditions among metrics, conjugate connections and
structure tensors. We demonstrate that distinct conjugate connections such as $h,\widetilde{h},J$ and $J^{\ast }-$conjugates, may yield quasi-statistical manifolds under appropriate compatibility assumptions. In particular, we establish a number of geometric results under the assumptions of Codazzi coupling and $d^{\nabla }$-closedness. The novelty of our approach lies in combining the framework of metallic-like manifolds with quasi-statistical structures in the presence of torsion, thereby extending
existing results in the literature and opening new directions for further research. Finally, we also present a theorem concerning the Tachibana operator, which highlights additional structural properties of the manifolds under consideration.

Keywords

Metallic-like Pseudo-Riemannian Manifolds , Quasi-Statistical Structures , Conjugate Connections , Codazzi Coupleds

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