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On the Limit Set of Discrete Subgroups of PU(2,1)

Authors:	J. -P. Navarrete

Affiliation:	(1) Universidad Nacional Autónoma de México, Mexico, D.F., Mexico

Abstract:	Let G be a discrete subgroup of PU(2,1); G acts on preserving the unit ball $mathbf H^2 _{mathbb C}$ , equipped with the Bergman metric. Let $L(G) subset S^3 = partial mathbf H^2 _{mathbb C}$ be the limit set of G in the sense of Chen–Greenberg, and let $Lambda(G) subset P^2_{mathbb C}$ be the limit set of the G-action on $P^2_{mathbb C}$ in the sense of Kulkarni. We prove that L(G) = Λ(G) ∩ S ³ and Λ(G) is the union of all complex projective lines in which are tangent to S ³ at a point in L(G).

Keywords:	Limit set Discrete subgroup Complex hyperbolic plane Complex hyperbolic geometry Complex projective plane
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