The Equivalence Problem for Five-dimensional Levi Degenerate CR Manifolds

Let M be a CR manifold of hypersurface type, which is Levi degenerate but also satisfying a k-nondegeneracy condition at all points. This might be only if dim M = 5 and if dim M = 5, then k= 2 at all points. We prove that for any five-dimensional, uniformly two-nondegenerate CR manifold M there exists a canonical Cartan connection, modeled on a suitable projective completion of the tube over the future light cone {z \in C^3 : (x_1)^2 + (x_2)^2 - (x_3)^2 = 0, x_3 > 0}. This determines a complete solution to the equivalence problem for this class of CR manifolds.