Journal
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
Volume 3, Issue 3, Pages 375-420Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S021988780600117X
Keywords
symplectic connections; special symplectic connections; preferred connections; Ricci-type; Ricci-flat; symplectic reduction; symplectic induction; twistors; strict deformation quantization
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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,non-commutative symplectic symmetric spaces.
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