A characterization of Fuchsian groups acting on complex hyperbolic spaces
Xi Fu, Liulan Li, Xiantao Wang (2012)
Czechoslovak Mathematical Journal
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Let be a non-elementary complex hyperbolic Kleinian group. If preserves a complex line, then is -Fuchsian; if preserves a Lagrangian plane, then is -Fuchsian; is Fuchsian if is either -Fuchsian or -Fuchsian. In this paper, we prove that if the traces of all elements in are real, then 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...