2014 Fiscal Year Final Research Report
Fisher information geometry of Riemannian manifolds and Poisson kernel, heat kernel
| Project/Area Number |
24540065
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | Fisher 計量 / Hadamard 多様体 / 理想境界 / Busemann 関数 / Poisson 核 / 漸近調和 / 双曲空間 / 体積エントロピー |
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| Outline of Final Research Achievements |
We developed geometry of horospheres, level hypersurfaces of Busemann function and obtained rigidity theorems of real, complex, quaternionic hyperbolic spaces in terms of volume entropy These results are consequence of the identity theorem of volume entropy and horosphere mean curvature for an asymptotically harmonic Hadamard manifold. We obtained information geometry of barycenter map on ideal boundary of an Hadamard manifold by using theory developed by T.Friedrich.
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| Free Research Field |
Differential Geometry
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