  We consider complex projective structures on Riemann surfaces and their
groups of projective automorphisms. We show that the structures achieving the
maximal possible number of projective automorphisms allowed by their genus are
precisely the Fuchsian uniformizations of Hurwitz surfaces by hyperbolic
metrics. More generally we show that Galois Bely\u{\i} curves are precisely
those Riemann surfaces for which the Fuchsian uniformization is the unique
complex projective structure invariant under the full group of biholomorphisms.
