Jet Bundles as Higher-Order Polarised $k$-Contact Manifolds

We prove that the Cartan distribution $C^r_π$ on the jet bundle $J^rπ$, for $π:E\rightarrow Q$, is an $N^r_π$-contact distribution, where $N^r_π$ is the corank of $C^r_π$. In other words, $C^r_π$ has non-degenerate distributional curvature, and admits, locally, a complementary distribution spanned b