A Discreteness Condition for Subgroups of PU(2,1)

摘要

We establish a sufficient condition for a subgroup G = < A, B > of PU(2, 1) to be discrete, where the pair of isometries (A, B) is C-decomposable. This discreteness criterion is a complex hyperbolic version of Gilman's result in Gilman (Contemp Math 211:261-267, 1997). Furthermore, we give an example to show that one can use our method to ascertain the discreteness of groups that do not pass the classical discreteness test on isometric spheres.