Lecture Notes of Möbuis Transformation in Hyperbolic Plane

Rania B. M. Amer

Department of Engineering Mathematics and Physics, Faculty of Engineering, Zagazig University, Zagazig, Egypt.

DOI: 10.4236/am.2014.515215                

Abstract

In this paper, I have provided a brief introduction on M?bius transformation and explored some basic properties of this kind of transformation. For instance, M?bius transformation is classified according to the invariant points. Moreover, we can see that M?bius transformation is hyperbolic isometries that form a group action PSL (2, R) on the upper half plane model.

Keywords

The Upper Half-Plane Model, Möbius Transformation, Hyperbolic Distance, Fixed Points, The Group PSL (2, R)

Conflicts of Interest

The authors declare no conflicts of interest.

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