Complex and Quaternionic hyperbolic Kleinian groups with real trace fields

Joonhyung Kim, Sungwoon Kim

Let $\Gamma$ be a nonelementary discrete subgroup of SU(n,1) or Sp(n,1). We show that if the trace field of $\Gamma$ is contained in $\mathbb{R}$, $\Gamma$ preserves a totally geodesic submanifold…