Reduction, Induction and Ricci Flat Symplectic Connections

Abstract

In this paper we present a construction of Ricci-flat connections through an induction procedure. Given a symplectic manifold (M, ω) of dimension 2n, we define induction as a way to construct a symplectic manifold (P, μ) of dimension 2n + 2. Given any symplectic manifold (M, ω) of dimension 2n and given a symplectic connection ▽ on (M, ω), we define induction as a way to construct a symplectic manifold (P, μ) of dimension 2n+2 and an induced connection ▽P which is a Ricci-flat symplectic connection on (P, μ).