On a natural variational principle for symplectic connections

We review the article 'A variational principle for symplectic connections' of F. Bourgeois and M. Cahen. The aim is to select a set of preferred symplectic connections on two-dimensional symplectic manifolds by introducing a variational principle. We chose for a Lagrangian a polynomial in the curvature tensor of degree at most two. For compact surfaces we show that all solutions of the field equations must be locally symmetric. We then develop an equivalence between symmetric symplectic surfaces and symplectic symmetric triples and determine the list of isomorphism classes of two dimensional symplectic symmetric triples