Visualization of hyperbolic surfaces via generic fundamental polygons, and its applications on the theory of the canonical decomposition

通过通用基本多边形的双曲曲面可视化及其在正则分解理论中的应用

• 批准号: 21740047
• 负责人: USHIJIMA Akira
• 金额: $ 1.58万
• 依托单位: Kanazawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740047/
• 关键词: 双曲幾何学; 離散群; フックス群; 基本領域; クライン群

To visualize hyperbolic surfaces by using of computer, it is required to decide suitable symbolical treatment of such surfaces in this research. I obtained a prototype of such symbolical realization of, not only hyperbolic but also general, surfaces. An advantage of this realization is to detect hyperbolicity of surfaces. Another result is this research is that I obtained a proof of stability of the combinatorial type of generic fundamental polygons of Fuchsian groups when their centers are on the circle at infinity of the hyperbolic plane. This result corresponds to a known result of the same property of generic fundamental polygons with their centers in the hyperbolic plane.

为了利用计算机可视化双曲曲面，需要确定这类曲面的适当符号处理。我得到了一个原型，这种象征性的实现，不仅双曲，而且一般，表面。这种实现的优点是检测表面的双曲面。另一个结果是，当Fuchsian群的中心在双曲平面的无穷远点的圆上时，得到了Fuchsian群的一般基本多边形的组合型的稳定性的一个证明。这一结果对应于一个已知的结果相同的属性一般的基本多边形，其中心在双曲平面。

项目成果

Generic fundament alpolygons for Fuchsian groups

Fuchsian 群的通用基本四边形

• 发表时间: 2011
• 期刊: Pacific Journal of Mathematics in press
• 作者: Ushijima;A.
• 通讯作者: A.