English

A characterization of complex hyperbolic Kleinian groups in dimension 3 with trace fields contained in $\mathbb R$

Geometric Topology 2014-01-20 v1

Abstract

We show that Γ<SU(3,1)\Gamma < \textbf{SU}(3,1) is a non-elementary complex hyperbolic Kleinian group in which tr(γ)Rtr(\gamma) \in \R for all γΓ\gamma \in \Gamma if and only if Γ\Gamma is conjugate to a subgroup of SO(3,1)\textbf{SO}(3,1) or SU(1,1)×SU(2)\textbf{SU}(1,1)\times\textbf{SU}(2).

Cite

@article{arxiv.1401.4244,
  title  = {A characterization of complex hyperbolic Kleinian groups in dimension 3 with trace fields contained in $\mathbb R$},
  author = {Joonhyung Kim and Sungwoon Kim},
  journal= {arXiv preprint arXiv:1401.4244},
  year   = {2014}
}
R2 v1 2026-06-22T02:47:58.974Z