# Connections and jet fields

## TL;DR

This review explores various interpretations of connections in fiber and jet bundles, linking them to PDE systems and multivector fields, with a focus on linear and manifold connections.

## Contribution

It provides a comprehensive comparison of connection concepts across different geometric structures and their relation to differential equations.

## Key findings

- Different interpretations of connections in fiber and jet bundles
- Relation of connections to PDE systems and multivector fields
- Analysis of linear and manifold connections

## Abstract

In this review paper we discuss the different interpretations of the concept of connection in a fiber bundle and in a jet bundle, and relate it with first and second-order systems of partial differential equations (PDE's) and multivector fields. As particular cases we analyze the concepts of linear connections and connections in a manifold.