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 5-dimensional, uniformly 2-nondegenerate CR manifold M there exists a canonical Cartan connection, modelled 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.