关于Clifford交比及其应用

On Clifford Cross-Ration and Its Application

本文定义了Clifford交比,得到了n维空间的同胚为保向Mobius变换的充要条件和n维空间中四点共圆(或直线)的充要条件,并证明了Clifford交比的实部是n维保向Mobius变换的一个不变量.

By introducing Clifford cross-ration, we have given in this paper a suffiecent and necessary condition for that a homomorphism of R^n to R^n is a orientationperserving Mobius transtormation. It is proved that the real part of Clifford cross-ration is an invariant of an orientation-perserving Mobius transtormation.