Point invariants of third-order ODEs and hyper-CR Einstein-Weyl structures (Q478847)

The authors study when a scalar third-order ordinary differential equation defines a Lorentzian hyper-CR Einstein-Weyl structure. The answer is given in form of two relative point invariants given by a two- and a three-form, respectively, depending on derivatives of the equation up to order eight such that such a structure exists only when the Wünschmann invariant and these two new invariants vanish.