Symplectic connections
Abstract
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.
Cite
@article{arxiv.math/0511194,
title = {Symplectic connections},
author = {Pierre Bieliavsky and Michel Cahen and Simone Gutt and John Rawnsley and Lorenz Schwachhofer},
journal= {arXiv preprint arXiv:math/0511194},
year = {2007}
}
Comments
Version 2 removes the claim in section 6.8 that the twistor complex structure is compatible with reduction