2010 Fiscal Year Final Research Report
Euclidean cone structures on a surface and Teichmuller spaces
| Project/Area Number |
18540090
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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 | Kyushu University |
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Principal Investigator |
NISHI Haruko Kyushu University, 理学部, 准教授 (90274430)
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| Co-Investigator(Kenkyū-buntansha) |
OHSHIKA Ken'ichi 大阪大学, 大学院・理学研究科, 教授 (70183225)
OHBA Kiyoshi お茶の水女子大学, 理学部, 准教授 (80242337)
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| Research Collaborator |
NAGATOU Kaori 九州大学, 大学院・数理学研究院, 准教授 (40326426)
KOMORI Yohei 大阪市立大学, 大学院・理学研究科, 准教授 (70264794)
MIYACHI Hideki 大阪大学, 大学院・理学研究科, 准教授 (40385480)
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| Project Period (FY) |
2006 – 2010
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| Keywords | トポロジー / タイヒミュラー空間 / 平面多角形 |
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| Research Abstract |
The space of equivalence classes of complex structures on a surface is called Teichmuller space whose geometry is known to be very complicated. We study Teichmuller space through Euclidean cone-structures on a surface and try to show the one-to-one correspondence between Teichmuller space and the space of similarity classes of Euclidean polygons. As a result, we show an isomorphism between the Teichmuller space of one-pointed torus and the space of similarity classes of Euclidean quadrilaterals. Moreover we get a geometric structure induced by the area form on the polygons.
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