Isom $H^n$的离散无挠的子群的一个定理
A theorem on discrete, torsion free subgroups of Isom $H^n$
摘要：
设$H^n$是具有$n\geq 2$的双曲n-空间。设$Γ<Isom H^n$是离散的无挠的子群，$a$是不连续域$Ω(Γ)$中的一点.令$p$是从$H^n$到商流形$M=H^n/Γ$的投影映射。本文证明了在$H^n\cupΩ(Γ)$中存在$a$的开邻域$U$，使得$p$是$U\cap H^n$上的等距.
英文摘要：
Let $H^n$ be the hyperbolic n-space with $n\geq 2$. Suppose that $Γ<Isom H^n$ is a discrete, torsion free subgroup and $a$ is a point in the domain of discontinuity $Ω(Γ)$. Let $p$ be the projection map from $H^n$ to the quotient manifold $M=H^n/Γ$. In this paper we prove that there exists an open neighborhood $U$ of $a$ in $H^n\cupΩ(Γ)$ such that $p$ is an isometry on $U\cap H^n$.
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