Riemannian curvature of gaussian distribution in dual coordinate system

Prosper Rosaire Mama Assandje; Dongho Joseph; Thomas Bouetou Bouetou

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arXiv · 2507.08141

Riemannian curvature of gaussian distribution in dual coordinate system

Prosper Rosaire Mama Assandje·Dongho Joseph·Thomas Bouetou Bouetou

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Abstract

In this paper, we study the geometric nonlinearity properties, such as curvature and torsion, in a dual coordinate system of the Riemannian manifold defined by the Gaussian distribution. We also give the Amari formulas explicitly in this new coordinate system, which allows us to characterize existing geometric invariants, such as the dual potential function and the Fisher metric.

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BibTeX RIS

Prosper Rosaire Mama Assandje, Dongho Joseph, Thomas Bouetou Bouetou. 2025-07-10. Riemannian curvature of gaussian distribution in dual coordinate system. https://arxiv.org/abs/2507.08141

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