Reductions of some systems of differential equations determined by their symmetries (Q1120883)

The special systems of differential equations of the form \(\omega^{\alpha}\wedge \omega^{2\alpha}=\theta\) on a manifold \(M^{m+3}\) with principal form \(\omega^ 1,\omega^ 2,\theta,\omega^{\alpha}\) \((\alpha =3,...,m+2)\) are considered. It is shown that any symmetry of the system defines its reduction to a quasi linear system of equations of the first order. This construction is connected with Bäcklund transformations.