2017 Fiscal Year Final Research Report
Geometric studies on singularity of non-linear phenomena
| Project/Area Number |
26287009
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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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 |
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| Co-Investigator(Kenkyū-buntansha) |
大本 亨 北海道大学, 理学研究院, 教授 (20264400)
石川 剛郎 北海道大学, 理学研究院, 教授 (50176161)
佐治 健太郎 神戸大学, 理学研究科, 准教授 (70451432)
高橋 雅朋 室蘭工業大学, 工学研究科, 准教授 (80431302)
寺尾 宏明 北海道大学, 国際本部, 特任教授 (90119058)
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| Co-Investigator(Renkei-kenkyūsha) |
TONEGAWA Yoshihiro 東京工業大学, 理工学研究科, 教授 (80296748)
ONO Kaoru 京都大学, 数理解析研究所, 教授 (20204232)
UMEHARA Masaki 東京工業大学, 理工学研究科, 教授 (90193945)
KOIKE Shigeaki 東北大学, 理学研究科, 教授 (90205295)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | 非線形現象 / 特異性 / 幾何学 / ラグランジュ特異点 / ルジャンドル特異点 |
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| Outline of Final Research Achievements |
In this research project we have shown that Lagrangian equivalence among Lagrangian submanifold germs and a certain equivalence relation among the corresponding graph-like wave fronts are the same. Applications of this result include the classical differential geometry, the geometry of the space-time, the differential geometry of singular surfaces and mappings, and so on. On the other hand, a new application of singularity theory to quantum mechanics is also discovered in this research project.
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| Free Research Field |
微分位相幾何学
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