Hengyang Normal University

About: Hengyang Normal University is a education organization based out in Hengyang, China. It is known for research contribution in the topics: Graphene & Adsorption. The organization has 1087 authors who have published 1280 publications receiving 13850 citations. The organization is also known as: Hengyang Teachers' College & Héngyáng Shīfàn Xuéyuàn.

A characterization of Fuchsian groups acting on complex hyperbolic spaces

Abstract: Let G ⊂ SU(2, 1) be a non-elementary complex hyperbolic Kleinian group. If G preserves a complex line, then G is ℂ-Fuchsian; if G preserves a Lagrangian plane, then G is ℝ-Fuchsian; G is Fuchsian if G is either ℂ-Fuchsian or ℝ-Fuchsian. In this paper, we prove that if the traces of all elements in G are real, then G is Fuchsian. This is an analogous result of Theorem V.G. 18 of B. Maskit, Kleinian Groups, Springer-Verlag, Berlin, 1988, in the setting of complex hyperbolic isometric groups. As an application of our main result, we show that G is conjugate to a subgroup of S(U(1)×U(1, 1)) or SO(2, 1) if each loxodromic element in G is hyperbolic. Moreover, we show that the converse of our main result does not hold by giving a ℂ-Fuchsian group.