  We consider invariant symplectic connections $\nabla$ on homogeneous
symplectic manifolds $(M,\omega)$ with curvature of Ricci type. Such
connections are solutions of a variational problem studied by Bourgeois and
Cahen, and provide an integrable almost complex structure on the bundle of
almost complex structures compatible with the symplectic structure. If $M$ is
compact with finite fundamental group then $(M,\omega)$ is symplectomorphic to
$\P_n(\C)$ with a multiple of its K\"ahler form and $\nabla$ is affinely
equivalent to the Levi-Civita connection.
