关于Mоbius变换的分解

On the Decomposition of Mobius Transformations

本文得到了双曲元素的一种“平行”分解。利用此种几何分解，证明了Ｊｒｇｅｎｓｅｎ和Ｂｅａｒｄｏｎ关于Ｒｉｅｍａｎｎ面上短程线的一个结果在Ｈ￣３上成立。同时定义ｎ（ｎ＞２）维的空间半旋转，并讨论了ｎ维Ｍｏｂｉｕｓ变换关于空间半旋转的分解。

In this paper, we obtain a kind of “parallel”decomposition of hyperbolicelements. By use of this geometric decomposition,we prove that a result of Jrsengenand Beardon about geodesics in Riemann surface also holds in H￣3.We define the n-di-mensional(n>2) half-turns and discuss the decomposition of n-dimensional Mobiustransformations about n-dimensional half-turns.