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Local existence of statistical diffeomorphisms

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Title: Local existence of statistical diffeomorphisms
Authors: Satoh, Naoto1 Browse this author
Authors(alt): 佐藤, 直飛1
Keywords: information geometry
statistical diffeomorphism
statistical manifold
Hessian manifold
Issue Date: Feb-2019
Publisher: Pushpa Publishing House
Journal Title: JP Journal of Geometry and Topology
Volume: 22
Issue: 1
Start Page: 73
End Page: 95
Publisher DOI: 10.17654/GT022010073
Abstract: A diffeomorphism between statistical manifolds is said to be statistical if it preserves statistical structures. Our purpose is to find conditions that guarantee an extension of a given linear isomorphism between given tangent spaces to a local statistical diffeomorphism. In Riemannian geometry, it is known as the Cartan-Ambrose-Hicks theorem, which implies that a Riemannian metric is locally determined by its Riemannian curvature tensor. We generalize this theorem for statistical manifolds, and, in particular, for Hessian manifolds. We prove that a statistical structure is locally characterized by its Riemannian curvature tensor and difference tensor. Furthermore, we show that a Hessian structure is locally determined by its Hessian curvature tensor and difference tensor.
Type: article
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 佐藤 直飛

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