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Reduction,Induction and Ricci flat symplectic connections

Michel Cahen·Simone Gutt
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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 connection $\nabla$ on $(M,ω)$, we define an induced connection $\nabla^P$ which is a Ricci-flat symplectic connection on $(P,μ)$.

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Michel Cahen, Simone Gutt. 2005-09-01. Reduction,Induction and Ricci flat symplectic connections. https://arxiv.org/abs/math/0509014

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