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Symplectic connections

Pierre Bieliavsky·Michel Cahen·Simone Gutt·John Rawnsley·Lorenz Schwachhofer
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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.

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Pierre Bieliavsky, Michel Cahen, Simone Gutt, John Rawnsley, Lorenz Schwachhofer. 2006-05-16. Symplectic connections. https://arxiv.org/abs/math/0511194

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