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Symplectic connections

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Bieliavsky, Pierre [UCL] Cahen, M Gutt, S Rawnsley, J Schwachhofer, L

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.

Document type Communication à un colloque (Conference Paper) – Présentation orale avec comité de sélection
Publication date 2006
Language Anglais
Conference "20th International Workshop on Differential Geometric Methods in Theoretical Mechanics", Ghent(Belgium) (Aug 21-27, 2005)
Journal information "International Journal of Geometric Methods in Modern Physics" - Vol. 3, no. 3, p. 375-420 (2006)
Peer reviewed yes
issn 0219-8878
e-issn 1793-6977
Publisher World Scientific Publ Co Pte Ltd (Singapore)
Affiliation UCL - SC/MATH - Département de mathématique
Keywords Symplectic Connections ; Special Symplectic Connections ; Preferred Connections ; Ricci-type ; Ricci-flat ; Symplectic Reduction ; Symplectic Induction ; Twistors ; Strict Deformation Quantization
Links
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Bibliographic reference Bieliavsky, Pierre ; Cahen, M ; Gutt, S ; Rawnsley, J ; Schwachhofer, L. Symplectic connections.20th International Workshop on Differential Geometric Methods in Theoretical Mechanics (Ghent(Belgium), Aug 21-27, 2005). In: International Journal of Geometric Methods in Modern Physics, Vol. 3, no. 3, p. 375-420 (2006)
Permanent URL http://hdl.handle.net/2078.1/60008