| Project/Area Number |
15K17545
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Nippon Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
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| Keywords | アダマール多様体 / 確率測度の空間 / フィッシャー計量 / 重心 / 幾何平均 / 測地線 / 調和多様体 / 球フーリエ変換 / 体積エントロピー / α-接続 / α-測地線 / アフィン超曲面 / 一般化冪平均 / 双対接続構造 / 理想境界 |
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| Outline of Final Research Achievements |
(1) We defined the normalized geometric mean of two positive probability measures. By using this notion, we found that there exists the unique geodesic segment joining arbitrary two probability measures. Moreover, we showed that a geodesic segment belongs entirely to a fiber of the barycenter map on a Hadamard manifold, if and only if endpoints of the geodesic and its normalized geometric mean belong same fiber.
(2) We obtained some properties of geodesics with respect to alpha-connection on the space of all probability measures with positive density function.
(3) We defined a class of Harmonic manifolds of hypergeometric type and we developed the theory of the spherical Fourier transform on a Hadamard harmonic manifold which is of hypergeometric type.
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