Introduction to Conformal Geometry and Penrose Diagrams

Abstract

[en] Conformal geometry is the branch of mathematics that studies the transformations on manifolds that preserve the angles. It has a myriad of applications, both in mathematics and in physics. In this work we present an introduction to conformal geometry and describe its relation to Penrose diagrams, which are rep- resentations of spacetimes that preserve their causal structure. To this end, we start by providing the necessary tools for doing this work from semi-Riemannian geometry and conclude by giving examples of these diagrams.