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Journals / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 18 Issue: 1

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

Aydın Gezer(ATATURK UNIVERSITY, FACULTY OF SCIENCE)0000-0001-7505-0385
Olgun Durmaz(ERZURUM TECHNICAL UNIVERSITY, FACULTY OF SCIENCE)0000-0002-0913-3307
Buşra Aktaş(KIRIKKALE UNIVERSITY)0000-0002-1285-7250
Pages
—
Publication Date
2026-02-23
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Finally, we also present a theorem concerning the Tachibana operator, which highlights additional structural properties of the manifolds under consideration.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we investigate the conditions under which quasi-statistical structures can be realized on metallic-like pseudo-Riemannian manifolds.
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Key Findings & Data: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.
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Conclusion & Impact:Finally, we also present a theorem concerning the Tachibana operator, which highlights additional structural properties of the manifolds under consideration.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Metallic-like Pseudo-Riemannian Manifolds · Quasi-Statistical Structures · Conjugate Connections

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.

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Cite This Article

Gezer, A., Durmaz, O., Aktaş, B. (2026). Extending Information Geometry: Quasi-Statistical Structures on Metallic-Like Pseudo-Riemannian Manifolds. Turkish Journal of Mathematics and Computer Science, Volume: 18 Issue: 1. https://doi.org/10.47000/tjmcs.1789376

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