Abstract
We give an elementary construction of symplectic connections through reduction. This provides an elegant description of a class of symmetric spaces and gives examples of symplectic connections with Ricci type curvature, which are not locally symmetric; the existence of such symplectic connections was unknown.
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Baguis, P. and Cahen, M.: Marsden-Weinstein reduction for symplectic connections, Preprint ULB.
Cahen, M., Gutt, S. and Rawnsley, J.: Symmetric symplectic spaces with Ricci type curvature, In: G. Dito and D. Sternheimer (eds), Proceedings Conférence Moshé Flato 1999, Math. Phys. Stud. 22, Vol. 2, Kluwer Acad. Publ., Dordrecht, 2000, pp. 81-93.
De Vischer, M.: Mémoire de Licence, Bruxelles, 2000.
Vaisman, I.: Symplectic curvature tensors, Monatsch. Math. 100 (1985), 299-327
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Baguis, P., Cahen, M. A Construction of Symplectic Connections Through Reduction. Letters in Mathematical Physics 57, 149–160 (2001). https://doi.org/10.1023/A:1017997608735
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DOI: https://doi.org/10.1023/A:1017997608735