A Weierstrass type representation for surfaces via loop group method and its applications
| Project/Area Number |
26400059
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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 | Hokkaido University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 可積分曲面 / ループ群 / ワイエルシュトラス型の表現公式 / 停留曲面 / ソリトン方程式 / 極小曲面 / 曲線論 / 離散曲面 / ガウス曲率 / 離散化 / 曲面論 / 可積分系 / 調和写像 |
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| Outline of Final Research Achievements |
Surfaces whose structure equation can be given by an integrable system are often called integrable surfaces. Here the integrable systems is a generic term used to refer to solvable (partial) differential equations. In particular many integrable surfaces have a Weierstrass type representation in terms of loop groups and holomorphic functions.
In this research we studied integrable surfaces by using the Weierstrass type representation. Concretely, we studied affine harmonic maps, constant Gaussian curvature surfaces in 3-dimensional hyperbolic space, discrete affine spheres, affine plane curves and maximal surfaces in 3-dimensional Anti-de Sitter space.
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Report
(5 results)
Research Products
(28 results)
