The equivalence problem for five-dimensional Levi degenerate CR manifolds (Q2929654)

While it is a classical result, going back to Cartan, Tanaka and Chern and Moser, that Levi-nondegenerate CR manifolds of hypersurface type possess a canonical Cartan connection, the same problem for Levi-degenerate CR manifolds has been open for a long time. The first instance of a uniformly Levi-degenerate CR geometry occurs in dimension 5. The authors construct a canonical Cartan connection for 5-dimensional uniformly Levi-degenerate CR manifolds. In particular, this solves the equivalence problem for this class of CR manifolds.