Complex and Quaternionic hyperbolic Kleinian groups with real trace fields

Joonhyung Kim; Sungwoon Kim

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arXiv · 1412.7918

Complex and Quaternionic hyperbolic Kleinian groups with real trace fields

Joonhyung Kim·Sungwoon Kim

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Abstract

Let $Γ$ be a nonelementary discrete subgroup of SU(n,1) or Sp(n,1). We show that if the trace field of $Γ$ is contained in $\mathbb R$, $Γ$ preserves a totally geodesic submanifold of constant negative sectional curvature. Furthermore if $Γ$ is irreducible, $Γ$ is a Zariski dense irreducible discrete subgroup of SO(n,1) up to conjugation. This is an analog of a theorem of Maskit for general semisimple Lie groups of rank $1$.

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BibTeX RIS

Joonhyung Kim, Sungwoon Kim. 2015-01-29. Complex and Quaternionic hyperbolic Kleinian groups with real trace fields. https://arxiv.org/abs/1412.7918

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