| Project/Area Number |
15K04836
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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 | Utsunomiya University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
AIHARA Yosihiro 福島大学, 人間発達文化学類, 教授 (60175718)
UMEHARA Masaaki 東京工業大学, 大学院情報理工学研究科, 教授 (90193945)
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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 |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 微分幾何 / 部分多様体 / 平坦トーラス / ３次元球面 / 直径 / 剛性 / 正則閉曲線 / ２重接触 / 微分幾何学 |
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| Outline of Final Research Achievements |
Diameter conjecture on flat tori in the unit 3-sphere states that the extrinsic diameter of isometrically immersed flat tori in the unit 3-sphere is equal to π. To prove this conjecture, it is sufficient to prove bi-tangent conjecture on periodic admissible pairs (c_1,c_2) in the unit 2-sphere, which states that if the self-intersection numbers of the closed curves c_1 and c_2 are odd, then c_1 and c_2 have a bi-tangent of the second kind．In this research, we study bi-tangent conjecture on periodic admissible pairs (c_1,c_2), and we proved that the conjecture is true if the curve c_1 contains an negative shell.
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