{"paper":{"title":"Complex and Quaternionic hyperbolic Kleinian groups with real trace fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Joonhyung Kim, Sungwoon Kim","submitted_at":"2014-12-26T09:31:52Z","abstract_excerpt":"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 of constant negative sectional curvature. Furthermore if $\\Gamma$ is irreducible, $\\Gamma$ 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 $1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7918","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}