Connection theory on differentiable fibre bundles. A pedagogical introduction

TL;DR

This paper provides a pedagogical review of connection theory on differentiable fibre bundles, focusing on linear connections on vector bundles and their local representations in various frames.

Contribution

It offers an accessible introduction to the complex concepts of connection theory, emphasizing local representations and frame adaptations for better understanding.

Findings

Clarifies the local representation of connections in different frames

Highlights the role of linear connections on vector bundles

Provides an educational overview of connection theory concepts

Abstract

The paper contains a review on the general connection theory on differentiable fibre bundles. Particular attention is paid to (linear) connections on vector bundles. The (local) representations of connections in frames adapted to holonomic and arbitrary frames is considered.