We consider Legendrian contact structures on odd-dimensional complex analytic manifolds. We are particularly interested in integrable structures, which can be encoded by compatible complete systems of second order PDEs on a scalar function of many independent variables and considered up to point transformations. Using the techniques of parabolic differential geometry, we compute the associated ...

We classify all (locally) homogeneous Levi non-degenerate real hypersurfaces in C³ with symmetry algebra of dimension ≥6.