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Local existence of statistical diffeomorphisms
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 |
URI: | http://hdl.handle.net/2115/75440 |
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)
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Submitter: 佐藤 直飛
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