摘要
本文利用高维Ｍｂｉｕｓ变换的 Ｃｌｉｆｆｏｒｄ矩阵表示，讨论了高维 Ｍｂｉｕｓ变换的正则性；证明了三维抛物Ｍｂｉｕｓ变换一定是正则的，得到了三维非抛物Ｍｂｉｕｓ变换是正则的一条充要条件；同时举例说明上述充要条件在ＳＬ（２， ｎ）（ｎ＝２ｋ，ｋ≥２）中不成立．
In this paper, by using the Clifford matrix representation of higher dimensional Mobius transformations, we discuss the regularity of n dimensional Mobius transformations. We prove that each three dimensional parabolic Mobius transformation is regular. Also we obtain a necessary and sufficient condition for three dimensional nonparabolic Mobius transformations to be regular. In the end, we construct an example to show that the above necessary and sufficient condition does not hold in SL(2, n ) when n = 2k, k 2.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2000年第2期309-316,共8页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金!19801011
湖南省科学基金!98JJY2072
