  Given a compact Kaehler manifold X, it is shown that pairs of the form (E,
D), where E is a trivial holomorphic vector bundle on X, and D is an integrable
holomorphic connection on $E$, produce a neutral Tannakian category. The
corresponding pro-algebraic affine group scheme is studied. In particular, it
is shown that this pro-algebraic affine group scheme for a compact Riemann
surface determines uniquely the isomorphism class of the Riemann surface.
