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 $\mathrm{\nabla }$ on $(M,\omega )$, we define an induced connection ${\mathrm{\nabla }}^P$ which is a Ricci-flat symplectic connection on $(P,\mu )$.