We build a canonical family {
Ds } 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
dD*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.
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