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.

引用

页码：433 / 453

页数：21

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