Research on Contact Web Theory and Related Geometric Structures as Foundations of Theory of Differential Equations
| Project/Area Number |
25400067
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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 | Nagoya University |
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Principal Investigator |
SATO Hajime 名古屋大学, 多元数理科学研究科, 名誉教授 (30011612)
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| Co-Investigator(Renkei-kenkyūsha) |
OZAWA Tetsuya 名城大学, 理工学部, 教授 (20169288)
SUZUKI Hiroshi 名古屋大学, 多元数理科学研究科, 准教授 (70235993)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | ルジャンドル織物 / グロンウォール予想 / 3階常微分方程式 / シュワルツ微分 / 接触射影幾何 / 線形化 / グロンオール予想 / シンプレクティック多様体 / ラグランジアン織物 / サミュエルソン条件 / 接触織物 / ジェット空間 / 最大等方空間 |
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| Outline of Final Research Achievements |
The uniqueness problem of linearizations of planar 3-webs under projective transformations is called Gronwall conjecture and still open for more than 100 years. Our research is concerned with Legendrian 3-webs on the 3-dimensional contact space. We proved the uniqueness of linearization map under contact projective transformations for Legendrian d-web when d is greater than 3. This solves the Gronwall conjecture in the (restricted) case above. The proof is given by showing the fundamental theorems, one by one, of contact projective geometry corresponding to those of planar projective geometry.
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Report
(4 results)
Research Products
(17 results)
