Jet bundle

Summary

The $k$-th jet bundle of a fiber bundle $E \to M$ is the manifold of all $k$-jets of local sections of $E$. A point of it records a point of $M$, a value in the fiber and all derivatives up to order $k$ of a section there. It is the natural home of differential equations on bundles: an equation of order $k$ is a subset of the $k$-th jet bundle. Jet bundles are used in the calculus of variations, in the geometric theory of partial differential equations and in field theory.