摘要

In this paper, four new discreteness criteria for isometric groups on complex hyperbolic spaces are proved, one of which shows that the Condition C hypothesis in Cao ['Discrete and dense subgroups acting on complex hyperbolic space', Bull. Aust. Math. Soc. 78 (2008), 211-224, Theorem 1.4] is removable; another shows that the parabolic condition hypothesis in Li and Wang ['Discreteness criteria for Mobius groups acting on (R) over bar (n) II', Bull. Aust. Math. Soc. 80 (2009), 275-290, Theorem 3.1] is not necessary.

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