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arXiv · 2103.10102

The Bonnet theorem for statistical manifolds

Taiji Marugame
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Abstract

We prove the Bonnet theorem for statistical manifolds, which states that if a statistical manifold admits tensors satisfying the Gauss--Codazzi--Ricci equations, then it is locally embeddable to a flat statistical manifold (or a Hessian manifold). The proof is based on the notion of statistical embedding to the product of a vector space and its dual space introduced by Lauritzen. As another application of Lauritzen's embedding, we show that a statistical manifold admitting an affine embedding of codimension 1 or 2 is locally embeddable to a flat statistical manifold of the same codimension.

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Taiji Marugame. 2021-03-18. The Bonnet theorem for statistical manifolds. https://arxiv.org/abs/2103.10102

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