Mobius变换的推广及其几何性质

The Generalization and Its Geometric Properties of Mobius Transformation

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.