2011 Fiscal Year Final Research Report
Global construction of constant mean curvature surfaces in terms of contact geometry and loop groups
| Project/Area Number |
21540067
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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 | Yamagata University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Keywords | 平均曲率一定曲面 / 接触幾何学 / ループ群 / 調和写像 / DPW法 |
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| Research Abstract |
We showed that minimal surfaces in hyperbolic 3-space are obtained as projections of f-holomorphic curves in the semi-Riemannian homogeneous contact space SL (2,C)/U(1). By using the appropriate loop group splitting, for any prescribed potential, we can construct f-holomorphic curves in SL (2,C)/U(1). It is shown that non-minimal constant mean curvature surfaces with mean curvature less than 1 can be obtained from f-holomorphic curves. By using this loop group method (new DPW-method), we constructed radially symmetric constant mean curvature surfaces in hyperbolic 3-space. We classified minimal translation surfaces in the 3-dimensional Heisenberg group.
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[Presentation] 差分幾何2011
Author(s)
井ノ口順一
Organizer
日本数学会幾何学分科会第58回幾何学シンポジウム
Place of Presentation
山口大学
Year and Date
2011-08-30
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