Quaternionic hyperbolic Fuchsian groups

@article{Kim2011QuaternionicHF,
  title={Quaternionic hyperbolic Fuchsian groups},
  author={Joonhyun Kim},
  journal={Linear Algebra and its Applications},
  year={2011},
  volume={438},
  pages={3610-3617}
}
  • Joonhyun Kim
  • Published 31 December 2011
  • Mathematics
  • Linear Algebra and its Applications
The complex hyperbolic Kleinian groups with an invariant totally geodesic submanifold
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IfGamma is irreducible, it is shown that if the trace field of $\Gamma$ is contained in R, it preserves a totally geodesic submanifold of constant negative sectional curvature.
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In this notes, we characterize discrete subgroups of PU(2,1), holomorphic isometric group of complex hyperbolic space, which have an invariant totally geodesic submanifold.
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Let G ⊂ SU(2, 1) be a non-elementary complex hyperbolic Kleinian group. If G preserves a complex line, then G is ℂ-Fuchsian; if G preserves a Lagrangian plane, then G is ℝ-Fuchsian; G is Fuchsian if
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