Homogeneous symplectic manifolds with Ricci - type curvature

We consider invariant symplectic connections ∇ on homogeneous symplectic manifolds (M, ω) 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, ω) is symplectomorphic to P n (C) with a multiple of its Kähler form and ∇ is affinely equivalent to the Levi-Civita connection. Research of the first three authors supported by an ARC of the communauté française de Belgique.