Symplectic space forms and submanifolds
This is a report on some ongoing work with Michel Cahen and Thibaut Grouy: the aim of our project is to define Radon-type transforms in symplectic geometry. The chosen framework is that of symplectic symmetric spaces whose canonical connection is of Ricci-type. These can be considered as symplectic analogues of the space forms, i.e. the spaces of constant sectional curvature, in Riemannian geometry. I shall focus here on their submanifold theory and I shall recall constructions of models of such spaces.