LAUSR

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