Study on Riemann surfaces and Klein surfaces with hyperbolic regular polygons as their fundamental regions

以双曲正多边形为基本区域的黎曼曲面和克莱因曲面研究

• 批准号: 20740081
• 负责人: NAKAMURA Gou
• 金额: $ 2.58万
• 依托单位: Aichi Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20740081/
• 关键词: 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

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.

解决了极值Klein曲面中嵌入了多少个极值圆盘的问题，并根据极值圆盘的个数、位置和自同构群对曲面进行了分类.为此，我们使用双曲正多边形作为其基本区域。对于亏格为2的双曲正多边形Riemann曲面，通过基于Weierstrass点重构基本区域，给出了Teichmuller空间方程和曲面的齐次坐标。

项目成果

Compact non-orientable surfaces of genus 5 with extremal metric discs

具有极值公制圆盘的 5 类致密不可定向表面

• 发表时间: 2012
• 期刊: Glasgow Math. J
• 作者: Jun Kato;加藤淳;Gou Nakamura
• 通讯作者: Gou Nakamura

Compact Klein surfaces of genus 5 with extremal disc Joint Mathematics Meetings

具有极值盘的 5 型紧克莱因面联合数学会议

• 发表时间: 2011
• 作者: Jun Kato;加藤淳;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;中西敏浩;中西敏浩;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura
• 通讯作者: Gou Nakamura

Parametrizations of Teichmuller spaces by trace functions

通过迹函数对 Teichmuller 空间进行参数化

• 发表时间: 2011
• 作者: Osamu Hatori;Yasuo Iida;中西敏浩;Ryu Sasaki;Y.Morimoto;Osamu Hatori and Lajos Molnar;Ryu Sasaki;Toshihiro Nakanishi
• 通讯作者: Toshihiro Nakanishi

Trace parameters for Teichmuller space

Teichmuller 空间的迹参数

• 发表时间: 2011
• 作者: Jun Kato;加藤淳;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;中西敏浩
• 通讯作者: 中西敏浩

Automorphism groups of q-m-gonal planar Klein surfaces

q-m-角平面克莱因曲面的自同构群

• 发表时间: 2010
• 作者: Jun Kato;加藤淳;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;中西敏浩;中西敏浩;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura;Gou Nakamura
• 通讯作者: Gou Nakamura