Studies on some open problems concerning flat tori in odd dimensional spheres
| Project/Area Number |
24540066
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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 Yoshihiro 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) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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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 / 直径予想 / 剛性定理 / 正則閉曲線 / ２重接触 / 微分幾何学 / 直径 / 剛性 |
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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. In 2011, we obtained a theorem which states that the conjecture is true under the assumption that the mean curvature of the immersion is nonnegative or nonpositive. Unfortunately, there was a gap in the proof of a proposition which was a key assertion to prove the theorem. In this research, using a new lemma on the shape of simple loops in the unit 2-sphere, we corrected the proof of the proposition. As a result, we established the theorem.
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Report
(4 results)
Research Products
(5 results)
