Images of circles, lines, balls and half-planes under Mobius transformations

TL;DR

This paper investigates how Mobius transformations map geometric objects like circles, lines, balls, and half-planes, providing insights into their geometric properties and transformations.

Contribution

It offers a detailed analysis of the images of various geometric objects under Mobius transformations, highlighting their properties and behaviors.

Findings

Characterization of images of circles and lines under Mobius transformations

Descriptions of how balls and half-planes are transformed

Insights into the geometric invariants preserved by Mobius transformations

Abstract

In the paper, we study the images of circles, lines, balls and half-planes under Mobius transformations.