  We extend T. Y. Thomas's approach to the projective structures, over the
complex analytic category, by involving the $\rho$-connections. This way, a
better control of the projective flatness is obtained and, consequently, we
have, for example, the following application: if the twistor space of a
quaternionic manifold $P$ is endowed with a complex projective structure then
$P$ can be locally identified, through quaternionic diffeomorphisms, with the
quaternionic projective space.
