复双曲Klein群是作用在复双曲空间上的离散等距群.本项目将主要研究以下三个方面的问题：1、研究复双曲(3,3,n)三角群的基本域在复双曲空间理想边界上的组合与几何性质，利用基本域的边配对关系得到相应的三维双曲流形；2、研究Parker-Will参数族群，特别是该参数群中一些重要子群和Unipotent曲线所对应的群，构造Ford基本多面体，并利用Poincare多面体定理来判断这些群的离散性；3、研究这些群的基本多面体在复双曲空间理想边界上的组合与几何性质，并得到所对应的三维双曲流形的球面CR单值化。

The complex hyperbolic Kleinian group is a discrete isometric group acting on the complex hyperbolic space. In this project we will study the following three problems: 1.We will study the combination and geometry of the fundamental domain at the ideal boundary of complex hyperbolic space of the complex hyperbolic triangle group (3,3,n). We will identify the hyperbolic 3-manifold from the side-pairings of the the fundamental domain；2. We will study the Parker-Will's family groups with parameters. In particular, we will consider some important subgroups and the groups on the Unipotent curve. In order to determine the discreteness of these groups, we need to construct the Ford fundamental domains and use the Poincare polyhedra theorem; 3.We will continue to study the combination and geometry of the fundamental domains at the ideal boundary of complex hyperbolic space and get the CR uniformization of these corresponding hyperbolic 3-manifolds.