Reduction,Induction and Ricci flat symplectic connections
  In this paper we present a construction of Ricci-flat connections through an induction procedure. Given a symplectic manifold $(M,\omega)$ of dimension $2n$, we define induction as a way to construct a symplectic manifold $(P,\mu)$ of dimension $2n+2$. Given any symplectic connection $\nabla$ on $(M,\omega)$, we define an induced connection $\nabla^P$ which is a Ricci-flat symplectic connection on $(P,\mu)$. 
Michel Cahen and Simone Gutt