Una Introducción geométrica a la teoría de Kaluza-Klein

Abstract

In this work, we introduce some of the mathematical foundations that are needed to develop the ancestor of unifying theories: Kaluza-Klein theory. We start summarizing the main concepts about smooth manifolds. After that, we include some notions about semi-Riemannian geometry, such as its metric, basic concepts like the affine connections and the construction of warped products. Only then, we are able to go deeper into the physical aspect of this work, introducing some elements of the Theory of Relativity which allow us to define the concept of space-time. Finally, we deal with the concept of a fiber bundle, which is essential for us to present the Kaluza-Klein spaces.