1. Introduction. Let S be an oriented closed surface of genus g > 1. A projec-tive structure on S is a maximal system of local coordinates modeled on the Riemann sphere C, whose transition functions are Möbius transformations. For a given pro-jective structure on S, we have a pair (f, ρ) of a local homeomorphism f from the universal cover S of S to C, called a developing map, and a group homomo...