Concrete construction of cone hyperbolic structures for a 3-dimensional cone manifold with non-compact cone singularity

具有非紧锥奇点的三维锥流形锥双曲结构的具体构造

• 批准号: 23740064
• 负责人: AKIYOSHI Hirotaka
• 金额: $ 1.58万
• 依托单位: Osaka City University (2012-2013)Kinki University (2011)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23740064/
• 关键词: 双曲幾何; クライン群; リーマン面; ３次元多様体; 錐双曲構造; トポロジー; 錐多様体

The space of complete cone hyperbolic structures on the 3-dimensional cone manifold obtained as the product of the torus with a single cone point and the interval has been studied, where a conjecture of Akiyoshi and Yamashita, which expects a certain relation between geometry and algebra, has been focused on. The following facts has been revealed: (1) The conjecture is true on the subspace consisting of real representations. (2) The simple loops are realized by geodesics for the cone hyperbolic structure associated with "good fundamental polyhedron". Moreover, certain bound on the lengths of geodesics are found. (3) The notion of Ford domain is generalized to the complete cone hyperbolic structures containing a "standard horospherical neighborhood", and the good fundamental polyhedra are shown to be the Ford domains.

研究了由单锥点与区间乘积得到的三维锥流形上的完全锥双曲结构的空间，其中Akiyoshi和Yamashita的猜想期望几何与代数之间存在某种关系，一直受到关注。揭示了以下事实： (1) 该猜想在由实数表示组成的子空间上成立。 (2)利用测地线实现了与“良好基本多面体”相关的锥双曲结构的简单环路。此外，还发现了测地线长度的一定界限。 (3)将福特域的概念推广到包含“标准星球邻域”的完整圆锥双曲结构，并证明良好的基本多面体是福特域。

项目成果

A concrete construction of cone hyperbolic structure

圆锥双曲结构的具体构造

• 发表时间: 2012
• 作者: Hirotaka Akiyoshi;Donghi Lee;and Makoto Sakuma;Hirotaka Akiyoshi;秋吉宏尚;秋吉宏尚;Hirotaka Akiyoshi;秋吉宏尚;秋吉宏尚;Hirotaka Akiyoshi
• 通讯作者: Hirotaka Akiyoshi

Towards the variation of Jorgensen's theory for the torus with a single cone point

走向约根森单锥点环面理论的变体

• 发表时间: 2014
• 作者: Hirotaka Akiyoshi;Donghi Lee;and Makoto Sakuma;Hirotaka Akiyoshi;秋吉宏尚
• 通讯作者: 秋吉宏尚

Towards the variation of Jorgensen’s theory for the torus with a single cone point

走向约根森单锥点环面理论的变体

• 作者: Hirotaka Akiyoshi;Donghi Lee;and Makoto Sakuma;Hirotaka Akiyoshi;秋吉宏尚;秋吉宏尚;Hirotaka Akiyoshi;秋吉宏尚;秋吉宏尚;Hirotaka Akiyoshi;秋吉宏尚;秋吉宏尚;秋吉宏尚;秋吉宏尚
• 通讯作者: 秋吉宏尚

A concrete construction of cone hyperbolic structure II

圆锥双曲结构II的具体构造

• 发表时间: 2013
• 作者: Hirotaka Akiyoshi;Donghi Lee;and Makoto Sakuma;Hirotaka Akiyoshi;秋吉宏尚;秋吉宏尚;Hirotaka Akiyoshi
• 通讯作者: Hirotaka Akiyoshi

錐双曲構造の具体的構成について

关于锥双曲结构的具体构型

• 发表时间: 2012
• 作者: Hirotaka Akiyoshi;Donghi Lee;and Makoto Sakuma;Hirotaka Akiyoshi;秋吉宏尚;秋吉宏尚;Hirotaka Akiyoshi;秋吉宏尚;秋吉宏尚;Hirotaka Akiyoshi;秋吉宏尚
• 通讯作者: 秋吉宏尚