On the uniqueness of the octonionic instanton solution on conformally flat 8-manifolds

LetMbe an 8-manifold and E be an SO(8) bundle on M. In a previous paper [F. Ozdemir and A.H. Bilge, "Self-duality in dimensions 2n > 4: equivalence of various definitions and the derivation of the octonionic instanton solution", ARI (1999) 51:247-253], we have shown that if the second Pontrjagin number p₂ of the bundle E is minimal, then the components of the curvature 2-form matrix F with respect to a local orthonormal frame are F_ij = c_ijω_ij, where c_ij's are certain functions and the ω_ij's are strong self-dual 2-forms such that for all distinct i, j, k, l, the products ω_ijω_jk are self dual and ω_ijω_kl are anti self-dual. We prove that if the c_ij's are equal to each other and the manifold M is conformally flat, then the octonionic instanton solution given in [B.Grossman, T.W.Kephart, J.D.Stasheff, Commun. Math. Phys., 96, 431-437, (1984)] is unique in this class