Study on discrete subgroups of PU(1,2;C) acting on complex hyperbolic 2-space

研究了复双曲2空间上PU（1,2；C）的离散子群。(1)找出群是离散的一些条件是很重要的。对于含有抛物型元的PU（1,2；C）子群，我们得到了Shimizu引理的复双曲形式。利用这种方法，我们可以构造一个精确不变的区域，这对于构造离散群的基本定义域是有用的。(2)研究了复双曲三角形群，讨论了它们的离散性。我们找到了几个离散的复双曲三角形群。

We have studied discrete subgroups of PU(1,2;C) acting on complex hyperbolic 2-space.(1) It is important to find out some conditions for a group to be discrete. For a subgroup of PU(1,2;C) containing a parabolic element, we obtain a complex hyperbolic version of Shimizu's lemma. Using this, we can construct a precisely invariant region, which is useful for construction of fundamental domain for a discrete group.(2) We have studied complex hyperbolic triangle groups and discussed their discreteness. We found several discrete complex hyperbolic triangle groups.