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Bieliavsky, Pierre, Cahen, M., Gutt, Simone, Rawnsley, John H. and Schwachhöfer, Lorenz (2006) Symplectic connections. In: 20th International Workshop on Differential Geometric Methods in Theoretical Mechanics, Ghent, Belgium, Aug 21-27, 2005. Published in: International Journal of Geometric Methods in Modern Physics, Vol.3 (No.3). pp. 375-420. doi:10.1142/S021988780600117X ISSN 0219-8878.
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Official URL: http://dx.doi.org/10.1142/S021988780600117X
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.
| Item Type: | Conference Item (Paper) | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | International Journal of Geometric Methods in Modern Physics | ||||
| Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||
| ISSN: | 0219-8878 | ||||
| Official Date: | May 2006 | ||||
| Dates: |
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| Volume: | Vol.3 | ||||
| Number: | No.3 | ||||
| Number of Pages: | 46 | ||||
| Page Range: | pp. 375-420 | ||||
| DOI: | 10.1142/S021988780600117X | ||||
| Status: | Not Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Conference Paper Type: | Paper | ||||
| Title of Event: | 20th International Workshop on Differential Geometric Methods in Theoretical Mechanics | ||||
| Type of Event: | Workshop | ||||
| Location of Event: | Ghent, Belgium | ||||
| Date(s) of Event: | Aug 21-27, 2005 |
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