A characterization of complex hyperbolic Kleinian groups in dimension 3 with trace fields contained in \(\mathbb{R}\)
The authors show that \(\Gamma<\text{SU}(3,1)\) is a non-elementary complex hyperbolic Kleinian group in which \(\text{tr}(\gamma)\in\mathbb{R}\) for all \(\gamma\in \Gamma\) if and only if \(\Gamma\) is conjugate to a subgroup of \(\text{SO}(3,1)\) or \(\text{SU}(1,1)\times \text{SU}(2)\). -- This result is an easy consequence of Satz 1 by [\textit{G. Kern-Isberner} and \textit{G. Rosenberger}, Result. Math. 6, 40--47 (1983; Zbl 0517.20023)].
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