arXiv subjects

Hitoshi Furuhata

Publications and source records attributed to Hitoshi Furuhata.

2 recordsLinked to original sources

arXiv2023

A Variation Problem for Mappings between Statistical Manifolds

We present statistical biharmonic maps, a new class of mappings between statistical manifolds naturally derived from a variation problem. We give the Euler-Lagrange equation of this problem and prove that improper affine hyperspheres induce examples of such maps.

math.DG↗

arXiv2020

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

We show that the statistical manifold of normal distributions is homogeneous. In particular, it admits a $2$-dimensional solvable Lie group structure. In addition, we give a geometric characterization of the Amari-Chentsov $α$-connections on the Lie group.

math.DG↗