The equivalence problem for higher-codimensional CR structures

Abstract

The equivalence problem for CR structures can be viewed as a special case of the equivalence problem for G-structure. This paper uses Cartan's methods (in modernized form) to show that a CR manifold of codimension 3 or greater with suitably generic Levi form admits a canonical connection on a reduced structure bundle whose group is isomorphic to the multiplicative group of complex numbers. As corollaries, it follows that the CR manifold admits a canonical affine connection, and consequently that the automorphisms of the CR manifold constitute a Lie group.