2011 Fiscal Year Final Research Report
Study on Riemann surfaces and Klein surfaces with hyperbolic regular polygons as their fundamental regions
| Project/Area Number |
20740081
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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 |
Basic analysis
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| Research Institution | Aichi Institute of Technology |
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Principal Investigator |
NAKAMURA Gou 愛知工業大学, 工学部, 准教授 (50319208)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 複素解析 / 関数論 / 解析学 / リーマン面 / クライン面 / 基本領域 / 極値的円板 |
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| Research Abstract |
We solved the problem that how many extremal discs are embedded in extremal Klein surfaces, and classified these surfaces by the number of extremal discs, location of extremal discs, and the group of automorphisms. For this aim we used hyperbolic regular polygons as their fundamental regions. As for Riemann surfaces of genus two with hyperbolic regular polygons we gave equations of the Teichmuller space and homogeneous coordinates for the surfaces by reconstructing fundamental regions based on the Weierstrass points.
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