The Bonnet theorem for statistical manifolds
| Autor: | Taiji Marugame |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Dual space Hessian manifolds Bonnet theorem The Gauss–Codazzi–Ricci equations Codimension The Bonnet theorem Statistical manifolds Mathematics::Geometric Topology Manifold Statistical manifold 53B12 (Primary) 53B25 (Secondary) Differential geometry Differential Geometry (math.DG) FOS: Mathematics Embedding Mathematics::Differential Geometry Mathematics::Symplectic Geometry Mathematics Vector space |
| DOI: | 10.1007/s41884-021-00056-4 |
| Popis: | 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. 10 pages |
| Databáze: | OpenAIRE |
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