Flat holomorphic connections on principal bundles over a projective manifold

Let G be a connected complex linear algebraic group and R-u(G) its unipotent radical. A principal G-bundle E-G over a projective manifold M will be called polystable if the associated principal G/R-u (G)-bundle is so. A G-bundle E-G over M is polystable with vanishing characteristic classes of degrees one and two if and only if E-G admits a flat holomorphic connection with the property that the image in G/ R-u(G) of the monodromy of the connection is contained in a maximal compact subgroup of G/ R-u(G).