Geometry of statistical structures and the submanifold theory
| Project/Area Number |
21540059
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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 | Hokkaido University |
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Principal Investigator |
FURUHATA Hitoshi 北海道大学, 理学(系)研究科(研究院), 准教授 (80282036)
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| Co-Investigator(Kenkyū-buntansha) |
KON Mayuko 信州大学, 教育学部, 准教授 (70507186)
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| Co-Investigator(Renkei-kenkyūsha) |
MATSUZOE Hiroshi 名古屋工業大学, 大学院工学研究科, 准教授 (90315177)
KUROSE Takashi 関西学院大学, 理工学部, 教授 (30215107)
HASEGAWA Izumi 北海道教育大学, 教育学部, 名誉教授 (50002473)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 統計多様体 / ヘッセ多様体 / ヘッセ断面曲率 / 複素空間形 / 部分多様体 / アファイン微分幾何学 / 微分幾何学 / 部分多様体論 / アファイン接続 / 統計はめ込み / 体様多計統 / 超曲面 / CR部分多様体 |
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| Research Abstract |
Geometry of statistical manifolds are deeply related to various research fields, for example, information geometry, affine differential geometry, and Hessian geometry. In this project, we researched the submanifold theoretical aspects of statistical manifolds, in particular, we studied construction and classification problems for Hessian manifolds of constant Hessian sectional curvature, and for statistical hypersurfaces between such spaces. Furthermore, through the study of Riemannian submanifolds in complex space forms, we prepared to build complex geometry for statistical manifolds.
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Report
(6 results)
Research Products
(69 results)
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[Book] 曲面2013
Author(s)
古畑仁
Total Pages
245
Publisher
数学書房
Related Report
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