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首页> 外文期刊>JP journal of geometry and topology >LOCAL EXISTENCE OF STATISTICAL DIFFEOMORPHISMS
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LOCAL EXISTENCE OF STATISTICAL DIFFEOMORPHISMS

机译：局部存在统计扩散族

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摘要

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.
机译：如果保留统计结构，则据说统计歧管之间的差异是统计歧义。 我们的目的是找到保证给给给定的切线空间与局部统计扩散的给定线性同构的延伸。 在riemannian几何中，它被称为Cartan-Ambrose-HICKS定理，这意味着黎曼曲率张量局部地确定。 我们概括了统计歧管的本定理，特别是对于黑森州歧管。 我们证明统计结构是局部地以其黎曼曲率张量和差异张量为特征。 此外，我们表明Hessian结构由其Hessian曲率张量和差异张量局部地确定。

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