Weakly maximal submodules of some S(V)-modules. Geometric applications (Q804056)

A k-th order system \(\Phi\) of partial differential equations on a fibered manifold is called weakly minimal, if for any k-th order system \(\Psi\) with \(\Phi\subset \Psi\) either \(\Psi\) is of finite type or the set of all integral \((k+p+1)-\)jets of \(\Psi\) is open in the set of all integral \((k+p+1)-\)jets of \(\Phi\) over any integral \((k+p)-\)jet of \(\Psi\). The author first studies the algebraic models for transitive systems of partial differential equations which are weakly minimal. Then the results are applied to some types of higher order G-structures and to certain foliations.