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The methods of Information geometry have been glowing up to develop various subjects of theoretical physics, including quantum information systems. The present article has two purposes. The first one is to develop general theory of homogeneous statis

Externí odkaz: http://arxiv.org/abs/2408.01647

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Homogeneous structures of $3$-dimensional Sasakian space forms

Autor: Inoguchi, Jun-ichi, Ohno, Yu

We give explicit parametrizations for all the homogeneous contact Riemannian structures on $3$-dimensional Sasakian space forms.

Externí odkaz: http://arxiv.org/abs/2408.01645

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Homogeneous Structures on $\mathbb{S}^2\times\mathbb{R}$ and $\mathbb{H}^2\times\mathbb{R}$

Autor: Ohno, Yu

We determine all the homogeneous structure tensors on $\mathbb{S}^2\times\mathbb{R}$ and $\mathbb{H}^2\times\mathbb{R}$. This work together with previous articles yields a complete classification of all the homogeneous structure tensors on three-dime

Externí odkaz: http://arxiv.org/abs/2307.05030

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A characterization of the alpha-connections on the statistical manifold of multivariate normal distributions

Autor: Kobayashi, Shimpei, Ohno, Yu

We study a statistical manifold $(\mathcal{N}, g^F, \nabla^{A}, \nabla^{A*})$ of multivariate normal distributions, where $g^F$ is the Fisher metric and $\nabla^{A}$ is the Amari-Chentsov connection and $\nabla^{A*}$ is its conjugate connection. We w

Externí odkaz: http://arxiv.org/abs/2302.07471

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On a constant curvature statistical manifold

Autor: Kobayashi, Shimpei, Ohno, Yu

We will show that a statistical manifold $(M, g, \nabla)$ has a constant curvature if and only if it is a projectively flat conjugate symmetric manifold, that is, the affine connection $\nabla$ is projectively flat and the curvatures satisfies $R=R^*

Externí odkaz: http://arxiv.org/abs/2008.13394

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