Homogeneous symplectic manifolds with Ricci-type curvature

Abstract

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.