Flat holomorphic connections on principal bundles over a projective manifold

Abstract

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 at 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).