2011 Fiscal Year Final Research Report
Riemannian Geometry and Information Geometry of Poisson kernels and heat kernels
| Project/Area Number |
21540065
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
SATO Hiroyasu 東京電機大学, 情報環境学部, 助教 (00375396)
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| Project Period (FY) |
2009 – 2011
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| Keywords | フィシャー情報計量 / ポアソン核 / 熱核 / 確率測度 / ビューズマン関数 / 漸近調和空間 / 体積エントロピー |
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| Research Abstract |
We investigated Riemannian geometry and Fisher information geometry of the Poisson kernel map φ from an Hadamard manifold X into the space P(∂X) of probability measures of positive density function, absolutely continous with respect to the Riemannian volume, defined on the ideal boundary of X. We obtained the following results : if the mapφ is homothetic and minimal, then the Poisson kernel is represented in terms of the Busemann function so that X turns out to be asymptotically harmonic and satisfies the axiom of visibility and furthermore we can show that this homothetic constant coincides with the volume entropy of X.
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