Symplectic connections
(2006) International Journal of Geometric Methods in Modern Physics — Vol. 3, n° 3, p. 375-420 (2006)
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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,non-commutative symplectic symmetric spaces.
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Bieliavsky, P., Cahen, M., Gutt, S., Rawnsley, J., & Schwachhofer, L. (2006). Symplectic connections. International Journal of Geometric Methods in Modern Physics, 3(3), 375-420. https://doi.org/10.1142/S021988780600117X (Original work published 2006)