Superstring effective actions and the central charge of the Virasoro algebra on a Kaehler manifold

We study higher-order corrections to the gravitational string effective action within a supersymmetric σ-model approach. We show that on a Kaehler manifold the corrections to the Einstein-Hilbert action vanish to all orders in α'. Moreover on such spaces the central charge of the Virasoro algebra is not perturbatively renormalized, once the corresponding gravitational equations of motion are satisfied. (orig.)