COMPLEX HYPERBOLIC (3, 3, n) TRIANGLE GROUPS

被引：12
|
作者：
Parker, John R. [1 ]
Wang, Jieyan [2 ]
Xie, Baohua [3 ]
机构：
[1] Univ Durham, Dept Math Sci, Durham DH1 3LE, England
[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
[3] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China
来源：
PACIFIC JOURNAL OF MATHEMATICS | 2016年 / 280卷 / 02期
关键词：
complex hyperbolic geometry; complex hyperbolic triangle groups; POLYHEDRA;
D O I：
10.2140/pjm.2016.280.433
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let p, q, r be positive integers. Complex hyperbolic (p, q, r) triangle groups are representations of the hyperbolic (p, q, r) reflection triangle group to the holomorphic isometry group of complex hyperbolic space H-C(2), where the generators fix complex lines. In this paper, we obtain all the discrete and faithful complex hyperbolic (3, 3, n) triangle groups for n >= 4. Our result solves a conjecture of Schwartz in the case when p = q = 3.
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页码：433 / 453
页数：21
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