On the Inhomogeneous Yang-Mills Equation d*<_D>R^D=f

We build a canonical family {D_s} of Hermitian connections in a Hermitian CR-holomorphic vector bundle (E,h) over a nondegenerate CR manifold M, parametrized by S∈Γ^∞(End(E)), S skewsymmetric. Consequently, we prove an existence and uniqueness result for the solution to the inhomogeneous Yang-Mills equation d*R^D=f on M. As an application we solve for D∈D(E,h) when E is either the trivial line bundle, or a locally trivial CR-holomorphic vector bundle over a nondegenerate real hypersurface in a complex manifold, or a canonical bundle over a pseudo-Einstein CR manifold