DISCRETENESS CRITERIA FOR ISOMETRIC GROUPS ACTING ON COMPLEX HYPERBOLIC SPACES

Abstract

AbstractIn 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 Möbius groups acting on$\overline {\mathbb {R}}^n$II’,Bull. Aust. Math. Soc.80(2009), 275–290, Theorem 3.1] is not necessary.