On H-balls and canonical regions of loxodromic elements in complex hyperbolic space
On H-balls and canonical regions of loxodromic elements in complex hyperbolic space
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复杂双曲空间中的H球和逆向元素的规范区域
DOI：
10.1017/s0305004100076210
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发表时间：
1993
影响因子：
0.8
通讯作者：
S. Kamiya
中科院分区：
文献类型：
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作者：
S. Kamiya
设U(1，n；ℂ)是的厄米特形式的自同构群。我们可以将U(1，n；ℂ)的一个元素看作作用于的变换，其中是复单位球的闭包。U(1，n；ℂ)的非平凡元素根据其不动点的数目和位置可分为三种共轭类型。设g是U(1，n；ℂ)的非平凡元。如果g在Bn中有不动点，我们称它为椭圆；如果g在Bn中有一个不动点，我们称g为抛物线，并且它位于边界∂Bn上。如果元素g恰好有两个不动点，且它们位于∂Bn上，则称g为斜交点。
Let U(1, n; ℂ) be the automorphism group of the Hermitian form for . We can regard an element of U(1, n; ℂ) as a transformation acting on , where is the closure of the complex unit ball The non-trivial elements of U(1, n; ℂ) fall into three conjugacy types, depending on the number and the location of their fixed points. Let g be a non-trivial element of U(1, n; ℂ). We call g elliptic if it has a fixed point in Bn and g parabolic if it has exactly one fixed point and this lies on the boundary ∂Bn. An element g will be called loxodromic if it has exactly two fixed points and they lie on ∂Bn.