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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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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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 / Fisher 情報計量 / 重心 / ホロ球 / ヤコビテンソル / ビューズマン関数 / 確率測度 / 情報幾何学 / ブーゼマン関数 / ダメック-リッチ空間 |
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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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Report
(4 results)
Research Products
(29 results)
