arXiv subjects

Yu Ohno

Publications and source records attributed to Yu Ohno.

7 recordsLinked to original sources

arXiv2025

The moduli spaces of left-invariant statistical structures on Lie groups

In the context of information geometry, the concept known as left-invariant statistical structure on Lie groups is defined by Furuhata--Inoguchi--Kobayashi (Inf Geom 4(1):177--188, 2021). In this paper, we introduce the notion of the moduli space of left-invariant statistical structures on a Lie group. We study the moduli spaces for three particular Lie groups, each of which has a moduli space of left-invariant Riemannian metrics that is a singleton. As applications, we classify left-invariant conjugate symmetric statistical structures and left-invariant dually flat structures (which are equivalent to left-invariant Hessian structures) on these three Lie groups. A characterization of the Amari--Chentsov $\alpha$-connections on the Takano Gaussian space is also given.

math.DG↗

arXiv2025

Homogeneous structures of $3$-dimensional Lie groups

We give a classification of homogeneous Riemannian structures on (non locally symmetric) $3$-dimensional Lie groups equipped with left invariant Riemannian metrics. This work together with classifications due to previous works yields a complete classification of all the homogeneous Riemannian structures on homogeneous Riemannian $3$-spaces. Two applications of the classification to contact Riemannian geometry and CR geometry are also given.

math.DG↗

arXiv2024

Homogeneous structures of $3$-dimensional Sasakian space forms

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

math.DG↗

arXiv2024

Homogeneous statistical manifolds

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 statistical manifolds. In particular we construct explicit examples of homogeneous statistical manifolds of low dimension. The second purpose is to classify $3$-dimensional Lie groups admitting non-trivial conjugate symmetric left invariant statistical structure.

math.DG↗

arXiv2023

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

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-dimensional homogeneous Riemannian manifolds.

math.DG↗

arXiv2023

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

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 will show that it admits a solvable Lie group structure and moreover the Amari-Chentsov connection $\nabla^{A}$ on $(\mathcal{N}, g^F)$ will be characterized by the conjugate symmetry, i.e., a curvatures identity $R=R^*$ of a connection $\nabla$ and its conjugate connection $\nabla^*$.

math.DG↗

arXiv2020

On a constant curvature statistical manifold

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 $R=R^*$, where $R^*$ is the curvature of the dual connection $\nabla^*$. Moreover, we will show that properly convex structures on a projectively flat compact manifold induces constant curvature $-1$ statistical structures and vice versa.

math.DG↗