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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 1

Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric

Vladimir Balan(University Politehnica of Bucharest)0000-0002-0124-4205
E. Peyghan(Arak University)0000-0002-2713-6253
Esa Sharahi(Arak University)0000-0002-1749-7469
Pages
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Publication Date
2020-02-06
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Several illustrative examples are provided, as well.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The first part of the paper is devoted to the classification of the statistical structures which live on the tangent bundle of a statistical manifold endowed with a Sasaki metric.
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Key Findings & Data:Further, considering a Kähler structure on the base statistical manifold, we introduce a family of almost complex structures on the tangent bundle equipped with the Sasaki metric, and find equivalent conditions for which this family induces a Kähler structure.
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Conclusion & Impact:Several illustrative examples are provided, as well.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Holomorphic statistical manifold · statistical structure · Kähler structure

Abstract

The first part of the paper is devoted to the classification of the statistical structures which live on the tangent bundle of a statistical manifold endowed with a Sasaki metric. Further, considering a Kähler structure on the base statistical manifold, we introduce a family of almost complex structures on the tangent bundle equipped with the Sasaki metric, and find equivalent conditions for which this family induces a Kähler structure. Finally, we derive equivalent conditions for existence of holomorphic structures on the tangent bundle equipped with the Sasaki metric in the presence of a statistical structure. Several illustrative examples are provided, as well.

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Cite This Article

Balan, V., Peyghan, E., Sharahi, E. (2020). Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 1. https://doi.org/10.15672/HJMS.2019.667

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