Pseudo-conformal quaternionic CR structure on (4n+3)-dimensional manifolds

We study an integrable, nondegenerate codimension 3-subbundle D on a ( 4n+3)manifold M whose fiber supports the structure of 4n-dimensional quaternionic vector space. It is thought of as a generalization of quaternionic C R structure. We single out an sp(1)- valued 1-form. locally on a neighborhood U such that Null omega = D vertical bar U and construct the curvature invariant on ( M, omega) whose vanishing gives a uniformization to flat quaternionic C R geometry. The invariant obtained on M has the same formula as that of pseudo-quaternionic Kahler 4n-manifolds. From this viewpoint, we exhibit a quaternionic analogue of Chern-Moser's C R structure.