Classical differential geometry from the modern viewpoint and its application
| Project/Area Number |
18540103
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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 | Fukuoka University |
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Principal Investigator |
KUROSE Takashi Fukuoka University, 理学部, 教授 (30215107)
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| Co-Investigator(Kenkyū-buntansha) |
SUAYMA Yoshihiko 福岡大学, 理学部, 教授 (70028223)
HAMADA Tatsuyoshi 福岡大学, 理学部, 助教 (90299537)
KAWAKUBO Satoshi 福岡大学, 理学部, 助教 (80360303)
MATSUURA Nozomu 福岡大学, 理学部, 助教 (00389339)
YAMADA Kotaro 東京工業大学, 大学院・理工学研究科, 教授 (10221657)
INOGUCHI Junichi 山形大学, 理学部, 准教授 (40309886)
FURUHATA Hitoshi 北海道大学, 大学院・理学研究院, 准教授 (80282036)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,080,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥780,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2006: ¥700,000 (Direct Cost: ¥700,000)
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| Keywords | 古典的微分幾何 / 可積分系 / 曲線の運動 / ハミルトン系 / 共形平坦超曲面 / 実超曲面 / ヘッセ幾何 / 情報幾何 / アフィン微分幾何 / ヘッセ多様体 / 差分幾何 / 離散化 / キルヒホッフ弾性棒 / 特異点 / 極大面 / 表現公式 / 統計多様体 / 平坦フロント / 零はめ込み / 等質空間 / 積分表示公式 / 差分KdV方程式 |
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| Research Abstract |
In this research, we studied classical differential geometry from modern viewpoints, such as of the theory of integral systems and of the theory of singularities ; we obtained results on various fields of classical differential geometry and their applications, in particular, the motions of curves associated with integrable systems, explicit construction and the classification of conformally flat hypersurfaces of four-dimensional space forms, real hypersurfaces of complex space forms, surfaces of three-dimensional spaces, affine differential geometry and its applications to Hessian geometry and information geometry, and so on.
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Report
(6 results)
Research Products
(50 results)
