Dualistic structures in information geometry

Léonard Todjihounde

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Submission date: 15. Nov. 2022
Pages: 20
Bibtex
MSC-Numbers: 53A15, 53B12, 53C15
Keywords and phrases: connections, statistical manifolds, metrics,, divergence functions, warped products, curvature
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Abstract:
We revisit some important basics of dualistic structures on Riemannian manifolds as a fundamental mathematical concept connecting information geometry, affine geometry and Hessian geometry. Since several statistical manifolds can be seen as warped product of spaces, we conclude this review by some results on warped products of dualistic structures.