5 citations · 16 across the 7 of their papers we have counts for
7 papers
Information geometry of the space of probability measures and barycenter maps
Mitsuhiro Itoh, Hiroyasu Satoh
In this article, we present recent developments of information geometry, namely, geometry of the Fisher metric, dualistic structures and divergences on the space of probability mea…
Hessian of the Busemann function on Damek-Ricci spaces
Hiroyasu Satoh
In this note, we calculate the Hessian of the Busemann function on a Damek-Ricci space. We investigate the eigenvalues of the Hessian and show its positive definiteness (Theorem 1)…
Harmonic manifolds of hypergeometric type and spherical Fourier transform
Mitsuhito Itoh, Hiroyasu Satoh
The spherical Fourier transform on a harmonic Hadamard manifold of positive volume entropy is studied. If is of hypergeometric type, namely spherical function…
Almost Hermitian structures on tangent bundles
Hiroyasu Satoh
In this article, we consider the almost Hermitian structure on induced by a pair of a metric and an affine connection on . We find the conditions under which admits al…
Harmonic Hadamard manifolds and Gauss hypergeometric differential equations
Mitsuhiro Itoh, Hiroyasu Satoh
A new class of harmonic Hadamard manifolds, those spaces called of hypergeometric type, is defined in terms of Gauss hypergeometric equations. Spherical Fourier transform defined o…
Geometric mean of probability measures and geodesics of Fisher information metric
Mitsuhiro Itoh, Hiroyasu Satoh
The space of all probability measures having positive density function on a connected compact smooth manifold , denoted by , carries the Fisher information metri…
Hessian of Busemann functions and rank of Hadamard manifolds
Mitsuhiro Itoh, Sinwhi Kim, JeongHyeong Park +1
In this article we show that every geodesic is rank one and the Hessian of Busemann functions is positive definite for a harmonic Damek-Ricci space, a two step solvable Lie group w…