| Project/Area Number |
21340016
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 Institute of Technology |
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Principal Investigator |
YAMADA Kotaro 東京工業大学, 理工学研究科, 教授 (10221657)
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| Co-Investigator(Renkei-kenkyūsha) |
UMEHARA Masaaki 大阪大学, 大学院・理学研究科, 教授 (90193945)
WAYNE Rossman 神戸大学, 理学部, 教授 (50284485)
YOSHIDA Masaaki 九州大学, 大学院・数理学研究院, 教授 (30030787)
KUROSE Takashi 福岡大学, 理学部, 教授 (30215107)
KOKUBU Masatoshi 東京電機大学, 工学部, 教授 (50287439)
FUJIMORI Shoichi 福岡教育大学, 教育学部, 講師 (00452706)
KAWAKAMI Yu 九州大学, 大学院・数理学研究院, 助教 (60532356)
HONDA Atsufumi 都城工業高等専門学校, 講師
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥15,340,000 (Direct Cost: ¥11,800,000、Indirect Cost: ¥3,540,000)
Fiscal Year 2013: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2012: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2011: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2010: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2009: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
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| Keywords | 曲面 / 特異点 / フロント / 特異曲率 / 連接接束 / ワイエルストラス表現 / 交叉帽子 / カスプ辺 / 双曲空間の平坦波面 / 極大曲面 / CMC-1 曲面 / ガウス・ボンネの定理 / 双曲計量 / 共形平坦計量 / 3ノイド / 超幾何微分方程式 / wave fronts / coherent tangent bundles / front bundles / Gauss-Bonnet formula / duality / conformally flat / comnplet / 特異点の微分幾何 |
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| Research Abstract |
We investigated, Weierstrass-type representation formula, global properties of several classes of surfaces with singularities, such as flat surfaces in hyperbolic 3-space, maximal surfaces in Minkowski 3-space, CMC-1 surfaces in de Sitter 3-space, and improper affine sphere in affine 3-space, and obtained a charctreization of completeness, Osserman-type inequalis etc.
In addition, flat trinoids in hyperbolic space and CMC-1 2-noids in de Sitter 3-space are classified. On the other hand, as a basic tool of differential geometry of wave front, we introduced a notion of "sinular curvature" and investigated a rdelationship between singular curvature and behavior of Gaussian curvature. As a result, we obtained Gauss-Bonnet type formula for wave fronts. Moreover, as an intrinsic formulation of wave fronts, we introduced a notion of "coherent tangent bundles" and gave an application of their duality.
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