Jets, frames, and their Cartan geometry

TL;DR

This paper develops a Cartan geometric framework for jet frames, linking gauge theory concepts with jet theory to provide new insights and interpretations in differential geometry.

Contribution

It introduces a Cartan geometric approach to jet frames, bridging gauge theory and jet theory in a novel way.

Findings

Provides a gauge-theoretic description of jet frames

Offers new geometric insights into the structure of jet spaces

Interpolates between gauge theory and jet theory concepts

Abstract

Jets frames, that is a generalisation of ordinary frames on a manifold, are described in a language similar to that of gauge theory. This is achieved by constructing the Cartan geometry of a manifold with respect to the diffeomorphism symmetry. This point of vue allows to give new insights and interpretations in the theory of jet frames, in particular by making an interpolation between ordinary gauge theory concepts and pure jet ones.