Differential geometric research on surfaces admitting singularities and its application
| Project/Area Number |
22540100
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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 | Tokyo Denki University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
UMEHARA Masaaki 東京工業大学, 大学院情報理工学研究科, 教授 (90193945)
YAMADA Kotaro 東京工業大学, 大学院理工学研究科, 教授 (10221657)
ROSSMAN Wayne 神戸大学, 大学院理学研究科, 教授 (50284485)
FUJIMORI Shoichi 岡山大学, 大学院自然科学研究科, 准教授 (00452706)
YAMAMOTO Ou 東京電機大学, 工学部, 教授 (20291700)
IRIE Hiroshi 東京電機大学, 未来科学部, 准教授 (30385489)
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| Project Period (FY) |
2010-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 微分幾何 / 平均曲率 / ガウス曲率 / 特異点 / 幾何学 |
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| Outline of Final Research Achievements |
We studied surfaces admitting singularities in some kind of three-dimensional manifolds of constant curvature, requiring them to have good properties from the differential-geometric viewpoint. (Note that non-Euclidean space of constant curvature have interesting features beyond our common sense.) Concerning linear Weingarten surfaces in hyperbolic space, we had a global representation formula, criterion for the shape of singularities, and a result on the orientability and the co-orientability. Concerning CMC-1 faces in de Sitter space and maxfaces in Lorentz-Minkowski space, we had results on the orientability and the co-orientability. At the same time, the classification of CMC-1 faces having two ends were obtained, and the classification of maxfaces having three ends were obtained.
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Report
(6 results)
Research Products
(9 results)
