Construction of surfaces in homogeneous spaces via spin geometry and loop groups
| Project/Area Number |
24540063
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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 | Yamagata University |
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Principal Investigator |
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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 |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | ループ群 / スピン幾何 / 曲面 / 調和写像 / DPW法 / ハイゼンベルグ群 / リーマン対称空間 / 重調和部分多様体 / 磁場付調和写像 / 曲線 / 接触幾何 / リー群 / 磁場 / ３次元球面 / 佐々木空間形 |
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| Outline of Final Research Achievements |
We showed that constancy of Gauss curvature of surfaces (of Gauss curvature less than 1) in the 3-sphere is characterized by the harmonicity of normal Gauss map. Based on this characterization, we established a loop group method for constructing negative constant Gauss curvature surfaces and surfaces of constant positive Gauss curvature (less than 1) in the 3-sphere simultaneously. We also obtain a loop group method for constructing surfaces of constant negative Gauss curvature (greather than -1) in hyperbolic 3-space. By combining spin geometry and loop group theory , we established a loop group method for constructing minimal surfaces in the 3-dimensional Heisenberg group. As an application, we give some new examples of minimal surfaces in the Heisenberg group.
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Report
(4 results)
Research Products
(24 results)
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[Presentation] 平面離散曲線の例について2014
Author(s)
井ノ口順一, 加藤慎也
Organizer
非線形波動研究の現状. 課題と展望を探る
Place of Presentation
九州大学応用力学研究所（福岡県春日市）
Year and Date
2014-10-31
Related Report
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