复双曲离散理想三角群  

The Discreteness of Complex Hyperbolic Ideal Triangle Groups

作　　者：黄小琳[1] 曹文胜[1] 

机构地区：[1]五邑大学数学与计算科学学院,广东江门529020

出　　处：《五邑大学学报（自然科学版）》2015年第4期10-15,共6页Journal of Wuyi University(Natural Science Edition)

基　　金：广东省自然科学基金资助项目(2015A030313644)

摘　　要：复双曲三角群是由3条复测地线上的复反射生成的,本文主要讨论复双曲理想三角群的离散性.通过复测地线相对应的极向量定义了角度参数,该角度不变量可以决定一个1 2 3(p,p,p)三角群,并由该角度不变量给出了复双曲空间中理想三角群离散的必要条件.Complex hyperbolic triangle groups are generated by three complex reflections of complex geodesics. This paper discusses the discreteness of complex hyperbolic ideal triangle groups. Using the polar vector of a complex geodesic, we construct an angular invariant. Such groups are parameterized by a real invariant α of triangles in the complex hyperbolic space. Furthermore, this angular invariant can uniquely determine a 1 2 3（ p, p, p）-triangle. Using the angular invariant, we obtain a necessary condition for a discrete embedding of a complex hyperbolic ideal triangle group.

关 键 词：复双曲空间 理想三角群 离散嵌入 角度不变量 

分 类 号：O151.21[理学—数学]