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 $\dim M\geq 5$ 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 $\{z\in \mathbb C^3:(x^1)^2+(x^2)^2-(x^3)^2=0,\ x^3 > 0\}$. This determines a complete solution to the equivalence problem for this class of CR manifolds.