Discreteness criteria for isometric groups of real and complex hyperbolic spaces

2009 ◽  
Vol 58 (3) ◽  
pp. 1443-1456 ◽  
Author(s):  
Shihai Yang ◽  
Ainong Fang
Keyword(s):  
Hyperbolic Spaces ◽  
Discreteness Criteria ◽  
Complex Hyperbolic Spaces

scholarly journals DISCRETENESS CRITERIA FOR ISOMETRIC GROUPS ACTING ON COMPLEX HYPERBOLIC SPACES

2010 ◽  
Vol 81 (3) ◽  
pp. 481-487
Author(s):  
XI FU
Keyword(s):  
Hyperbolic Space ◽  
Complex Hyperbolic Space ◽  
Hyperbolic Spaces ◽  
Discreteness Criteria ◽  
Condition C ◽  
Dense Subgroups ◽  
Complex Hyperbolic Spaces ◽  
Möbius Groups

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.

scholarly journals Incidence Axioms for the Boundary at Infinity of Complex Hyperbolic Spaces

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Sergei Buyalo ◽  
Viktor Schroeder
Keyword(s):  
Hyperbolic Space ◽  
Complex Hyperbolic Space ◽  
Hyperbolic Spaces ◽  
Complex Hyperbolic Spaces

Abstract We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.

scholarly journals Polar actions on complex hyperbolic spaces

2017 ◽  
Vol 287 (3-4) ◽  
pp. 1183-1213 ◽  
Author(s):  
José Carlos Díaz Ramos ◽  
Miguel Domínguez Vázquez ◽  
Andreas Kollross
Keyword(s):  
Hyperbolic Spaces ◽  
Polar Actions ◽  
Complex Hyperbolic Spaces

scholarly journals Homogeneous structures on real and complex hyperbolic spaces

2009 ◽  
Vol 53 (2) ◽  
pp. 561-574 ◽  
Author(s):  
M. Castrillón López ◽  
P. M. Gadea ◽  
A. F. Swann
Keyword(s):  
Hyperbolic Spaces ◽  
Homogeneous Structures ◽  
Complex Hyperbolic Spaces
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