# 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
8 Citations
The complex hyperbolic Kleinian groups with an invariant totally geodesic submanifold
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.
ON THE CONJUGACY OF MÖBIUS GROUPS IN INFINITE DIMENSION
• Mathematics
• 2016
In this paper, we establish some conjugacy criteria of groups in infinite dimension by using Clifford matrices. This extends the corresponding known results in finite dimensional setting.
A remark on a triple points in the boundary of quaternionic hyperbolic space
In this paper we consider a triple of distinct points in the boundary of quaternionic hyperbolic space and detect where these points are by using the quaternionic triple product.
A characterization of quaternionic Kleinian groups in dimension 2 with complex trace fields
• Mathematics
• 2016
Let $G$ be a non-elementary discrete subgroup of $\mathrm{Sp}(2,1)$. We show that if the sum of diagonal entries of each element of $G$ is a complex number, then $G$ is conjugate to a subgroup of
Complex and quaternionic hyperbolic Kleinian groups with real trace fields
• Mathematics
J. Lond. Math. Soc.
• 2016
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.
A characterization of complex hyperbolic Kleinian groups in dimension 3 with trace fields contained in $\mathbb R$
• Mathematics
• 2014
We show that $\Gamma < \textbf{SU}(3,1)$ is a non-elementary complex hyperbolic Kleinian group in which $tr(\gamma) \in \R$ for all $\gamma \in \Gamma$ if and only if $\Gamma$ is conjugate to a
Quaternionic hyperbolic Kleinian groups with commutative trace skew-fields
• Mathematics
Annals of Global Analysis and Geometry
• 2020
Let $$\Gamma$$ Γ be a nonelementary discrete subgroup of $${\mathrm {Sp}}(n,1)$$ Sp ( n , 1 ) . We show that if the trace skew-field of $$\Gamma$$ Γ is commutative, then $$\Gamma$$ Γ stabilizes a

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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.
Geometry of quaternionic hyperbolic manifolds
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Mathematical Proceedings of the Cambridge Philosophical Society
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We develop some of the basic theory of quaternionic hyperbolic geometry. We give necessary criteria for groups of quaternionic hyperbolic motions to be discrete. We give lower bounds on the volumes
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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
Cartan angular invariant and deformations of rank 1 symmetric spaces
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New geometric invariants in the quaternionic hyperbolic space and in the hyperbolic Cayley plane are introduced and studied. In these non-commutative and non-associative geometries they are a
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Mathematical Proceedings of the Cambridge Philosophical Society
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In this paper we consider quaternionic Möbius transformations preserving the unit ball in the quaternions $\bh$. In other words, maps of the form $g(z)=(az+b)(cz+d)^{-1}$ where $a$, $b$, $c$ and $d$
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