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 [5]. 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.
Mathematics Subject Classifications (2000): 53D35, 53D20, 58J60, 53C35