Symplectic connections

Details Symplectic connections Symplectic connections

2005-11-08

arxiv.org/abs/math/0511194v2

Mathematics

Symplectic Geometry

Version 2 removes the claim in section 6.8 that the twistor complex structure is compatible with reduction

Scientific paper

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.

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