This article is an overview of the results obtained in recent years on symplectic connections. We present what is known about preferred connections (critical points of a variational principle). The class of Ricci-type connections (for which the curvature is entirely determined by the Ricci tensor) is described in detail, as well as its far reaching generalization to special connections. A twistorial construction shows a relation between Ricci-type connections and complex geometry. We give a construction of Ricci-flat symplectic connections. We end up by presenting, through an explicit example, an approach to noncommutative symplectic symmetric spaces.
arXiv Mathematics e-prints
- Pub Date:
- November 2005
- Mathematics - Symplectic Geometry;
- Mathematics - Differential Geometry;
- Version 2 removes the claim in section 6.8 that the twistor complex structure is compatible with reduction