THE BOCHNER TYPE CURVATURE TENSOR OF PSEUDO CONVEX CR-STRUCTURES

Abstract

For a pseudo-convex $CR$-structure on an odd dimensional manifold, we introduce a family of canonical torsion-free linear connections. Every connection in this family is uniquely determined by an almost contact structure associated with the given pseudo convex $CR$-structure. We study the change of the connections in this family under the gauge transformations and, accordingly, the corresponding change of the gauge tensor fields. The Bochner type curvature tensor field we get is invariant under gauge transformations.