$f$-statistical connections and Miao-Tam statistical manifolds

Objective & Hypothesis:We introduce $f$-statistical connections as a family of statistical connections and study some geometric objects associated to these connections such as divergence, curvature and Ricci tensors, Hessian and Laplacian operators.

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Key Findings & Data:We construct examples of $f$-statistical connections and study the introducing concepts on them.

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Conclusion & Impact:Finally we introduce Miao-Tam statistical manifolds and study properties of them.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:f-statistical connction · Hessian operator · Laplacian operator

Abstract

We introduce $f$-statistical connections as a family of statistical connections and study some geometric objects associated to these connections such as divergence, curvature and Ricci tensors, Hessian and Laplacian operators. We construct examples of $f$-statistical connections and study the introducing concepts on them. Finally we introduce Miao-Tam statistical manifolds and study properties of them.

Keywords

f-statistical connction Hessian operator Laplacian operator Miao-Tam equation statistical manifold

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Cite This Article

Peyghan, E., Nourmohammadifar, L., Ali, A. (2025). $f$-statistical connections and Miao-Tam statistical manifolds. Hacettepe Journal of Mathematics and Statistics, Volume: 54 Issue: 2. https://doi.org/10.15672/hujms.1414765

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