Self-dual solutions to pseudo Yang–Mills equations

We study pseudo Yang Mills fields on a compact 5-dimensional strictly pseudoconvex CR manifold M i.e. critical points to the functional YMb(D) -1/2 integral(M)parallel to Pi R-H(D)parallel to(2) theta boolean AND (d theta)(2) on the space C(E,h) of all connections D on a Hermitian vector bundle (E, h) over M, such that Dh = 0. If A = {D epsilon C(E,h) : xi R-D = G(theta)(*) (Tr(R-D), d theta) = 0} and D epsilon A is an absolute minimum to YMb, A -> R then (i) Delta Tr-b(R-D) = 0 and (ii) D is self-dual or anti-self-dual according to the sign of c(2)(theta, D) = integral(M) theta boolean AND {P-2(D) - m-1/2m Pi (D) boolean AND P-1(D)} [where P-k (D) is the k-th Chern form of (E, D)] and provided c(2) (theta,D) is constant on A.