Spherical CR-manifolds of dimension 3

Abstract

A sphericalCR-structure on a smooth (2n−1)-manifoldM is a maximal collection of distinguished charts modeled on the boundary ∂H ℂ n of the complex hyperbolic space, where coordinate changes are restrictions of transformations from PU(n, 1). There exists a development map\(d:\tilde M \to \partial H_\mathbb{C}^n\), where\(\tilde M\) is the universal covering ofM, which is a local diffeomorphism. We study properties of the development maps and holonomy groups of sphericalCR-structures on compact 3-dimensional manifolds. We also give constructions of fundamental domains for some discrete subgroups of PU(2, 1).