2010 Fiscal Year Final Research Report
A construction of surfaces in spaces of constant curvature via integrable system method
| Project/Area Number |
20740045
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Hirosaki University |
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Principal Investigator |
KOBAYASHI Sinpei 弘前大学, 大学院・理工学研究科, 准教授 (40408654)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 平均曲率一定曲面 / ループ群 / 可積分系 / 線形常微分方程式 |
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| Research Abstract |
We defined complex constant mean curvature surfaces by a natural generalization of constant mean curvature surfaces in Euclidean three space and classified real form surfaces, such as constant mean curvature or constant Gauss curvature surfaces in spaces of constant curvature, for a complex constant mean curvature surface. We also characterized equivariant harmonic maps in complex projective spaces via potentials, which are matrix valued 1-forms. Moreover, a construction method of equivariant harmonic maps in complex projective spaces has been obtained from the potentials.
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