Mobius变换的推广及其几何性质  

The Generalization and Its Geometric Properties of Mobius Transformation

作　　者：潘国双[1] 赵成兵[1] 许忠义[1] 

机构地区：[1]南昌大学数学系,江西南昌330047

出　　处：《南昌大学学报（工科版）》2002年第3期43-46,共4页Journal of Nanchang University(Engineering & Technology)

基　　金：江西省自然科学基金资助项目(0011024)

摘　　要：先引入Mobius变换,讨论了此变换在复平面中的一些性质,接着把Mobius变换的实数形式推广到了n维空间,并证明了此推广即为共形变换.最后,讨论了Mobius变换在n维空间中的球几何和微分度量.In this paper,Mobius transformation is first introduced,and some properties are discussed about the transformation in the complex plane.Then we generalize the real number form of Mobius transformation to the n-dimensional space and prove that the generalization is just the conformation.In the end,we discuss the geometry of the sphere and the differential metric of Mobius transformation in the n-dimensional space.

关 键 词：几何性质 MOBIUS变换 实数形式 球几何 微分度量 共形变换 复平面 

分 类 号：O174.56[理学—数学]