Numerical flatness and principal bundles on Fujiki manifolds

Let M be a compact connected Fujiki manifold, G semisimple affine algebraic group over C with one simple factor and P fixed proper parabolic subgroup of G. For holomorphic principal G–bundle EG M, let EP the P–bundle EG⟶EG/P given by quotient map. We prove that following three statements are equivalent: (1) ad(EG) is numerically flat, (2) line bundle ⋀topad(EP)⁎ nef, (3) for every reduced irreducible complex analytic space Z Kähler form ω, map γ:Z⟶M, reduction structure EP⊂γ⁎EG to P, inequality degree(ad(EP))≤0 holds.