Zobrazeno 1 - 10
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pro vyhledávání: '"Satoh, Hiroyasu"'
Autor:
Satoh, Hiroyasu
Harmonic manifolds of hypergeometric type form a class of non-compact harmonic manifolds that includes rank one symmetric spaces of non-compact type and Damek-Ricci spaces. When normalizing the metric of a harmonic manifold of hypergeometric type to
Externí odkaz:
http://arxiv.org/abs/2405.05896
Autor:
Itoh, Mitsuhiro, Satoh, Hiroyasu
Publikováno v:
Sugaku Expositions 34 (2021), 231-253
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 measures, particularly the theory of geodesics of the Fisher metric. More
Externí odkaz:
http://arxiv.org/abs/2208.11861
Autor:
Satoh, Hiroyasu
In this note, we calculate the Hessian of the Busemann function on a Damek-Ricci space and show its positive definiteness (Theorem 5).
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/2110.08806
Autor:
Itoh, Mitsuhito, Satoh, Hiroyasu
Publikováno v:
Differential Geometry and its Applications, Volume 71, August 2020, 101646
The spherical Fourier transform on a harmonic Hadamard manifold $(X^n, g)$ of positive volume entropy is studied. If $(X^n, g)$ is of hypergeometric type, namely spherical functions of $X$ are represented by the Gauss hypergeometric functions, the in
Externí odkaz:
http://arxiv.org/abs/2005.13115
Autor:
Satoh, Hiroyasu
Publikováno v:
Proceedings of the Eleventh International Workshop on Differential Geometry, 105-118, Kyungpook Nat. Univ., Taegu, 2007
In this article, we consider the almost Hermitian structure on $TM$ induced by a pair of a metric and an affine connection on $M$. We find the conditions under which $TM$ admits almost K\"ahler structures, K\"ahler structures and Einstein metrics, re
Externí odkaz:
http://arxiv.org/abs/1908.10824
Autor:
Itoh, Mitsuhiro, Satoh, Hiroyasu
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 on a harmonic Hadamard manifold of hypergeometric type admits an invers
Externí odkaz:
http://arxiv.org/abs/1808.00625
Autor:
Itoh, Mitsuhiro, Satoh, Hiroyasu
Publikováno v:
Mathematische Nachrichten, Vol. 296, Issue 5 (2023), 1901-1927
The space of all probability measures having positive density function on a connected compact smooth manifold $M$, denoted by $\mathcal{P}(M)$, carries the Fisher information metric $G$. We define the geometric mean of probability measures by the aid
Externí odkaz:
http://arxiv.org/abs/1708.07211
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 with a left invariant metric. Moreover, the eigenspace of the Hessian o
Externí odkaz:
http://arxiv.org/abs/1702.03646
Autor:
Itoh, Mitsuhiro1 (AUTHOR), Satoh, Hiroyasu2 (AUTHOR) hiroyasu@nit.ac.jp
Publikováno v:
Mathematische Nachrichten. May2023, Vol. 296 Issue 5, p1901-1927. 27p.
Publikováno v:
In Journal of Environmental Management 15 June 2021 288