Contact structure on a jet bundle

Summary

The contact structure of a jet bundle is the family of contact forms: the $1$-forms that vanish on every prolonged section. Their common kernel is a distribution, called the contact or Cartan distribution. The contact forms tell the holonomic sections apart from all others. A section of the jet bundle is a prolongation exactly when it pulls back every contact form to zero. In the simplest case, the first jet bundle of functions of one variable, it is the standard contact structure on $\R^3$.