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pro vyhledávání: '"Mitsuhiro Itoh"'
Autor:
Mitsuhiro Itoh, Hiroyasu Satoh
Publikováno v:
Entropy, Vol 17, Iss 4, Pp 1814-1849 (2015)
Geometry of Fisher metric and geodesics on a space of probability measures defined on a compact manifold is discussed and is applied to geometry of a barycenter map associated with Busemann function on an Hadamard manifold \(X\). We obtain an explici
Externí odkaz:
https://doaj.org/article/863ed0b9dc274f1ebd22bcd13cf496fc
Autor:
Hiroyasu Satoh, Mitsuhiro Itoh
Publikováno v:
Sugaku Expositions. 34:231-253
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
Autor:
Hiroyasu Satoh, Mitsuhiro Itoh
Publikováno v:
Publications of the Research Institute for Mathematical Sciences. 55:531-564
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
Autor:
Hiroyasu Satoh, Mitsuhiro Itoh
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d7529ef8cbc523ebabafcb1af27d0efd
Publikováno v:
Kyushu Journal of Mathematics. 70:267-280
Publikováno v:
Differential Geometry and its Applications. 35:50-68
From geometrical study of horospheres we obtain, among asymptotically harmonic Hadamard manifolds, a rigidity theorem of the complex hyperbolic space C H m with respect to volume entropy. We also characterize C H m horospherically in terms of holomor
Autor:
Hiroyasu Satoh, Mitsuhiro Itoh
Publikováno v:
Kyushu Journal of Mathematics. 67:309-326
Publikováno v:
Taiwanese J. Math. 20, no. 4 (2016), 787-800
We give a construction which is Lie theoretic of anti-invariant Riemannian submersions from almost Hermitian manifolds, from quaternion manifolds, from para-Hermitian manifolds, from para-quaternion manifolds, and from octonian manifolds. This yields
Autor:
Hiroyasu Satoh, Mitsuhiro Itoh
Publikováno v:
Differential Geometry and its Applications. 29:S107-S115
Let ( X , g ) be an Hadamard manifold with ideal boundary ∂X. We can then define the map φ : X → P ( ∂ X ) associated with Poisson kernel on X, where P ( ∂ X ) is the space of probability measures on ∂X, together with the Fisher informatio
Publikováno v:
Proceedings of the American Mathematical Society. 136:3539-3548
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It is proved that the Hodge decomposition and Serre duality hold on a non-compact weighted CR manifold with negligible boundary. A complete CR manifold has negligible boundary. Some examples of complete CR manifolds are presented
It is proved that the Hodge decomposition and Serre duality hold on a non-compact weighted CR manifold with negligible boundary. A complete CR manifold has negligible boundary. Some examples of complete CR manifolds are presented