Remarks on Symplectic Connections

Abstract

This note contains a short survey on some recent work on symplectic connections: properties and models for symplectic connections whose curvature is determined by the Ricci tensor, and a procedure to build examples of Ricci-flat connections. For a more extensive survey, see Bieliavsky et al. [Int. J. Geom. Methods Mod. Phys. 3, 375–420 2006]. This note also includes a moment map for the action of the group of symplectomorphisms on the space of symplectic connections, an algebraic construction of a large class of Ricci-flat symmetric symplectic spaces, and an example of global reduction in a non-symmetric case.