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Gelfand, Israel; Retakh, Vladimir; Shubin, Mikhail

Fedosov manifolds. (English) Zbl 0945.53047

Adv. Math. 136, No. 1, 104-140 (1998).
A review of the geometry of Fedosov manifolds is given. A Fedosov manifold is a triple \((M,\omega,\Gamma)\), where \((M,\omega)\) is a symplectic manifold and \(\Gamma\) is a symplectic connection on \(M\). The famous result of B. V. Fedosov gives a canonical deformation quantization on such a manifold [see J. Differ. Geom. 40, No. 2, 213-238 (1994; Zbl 0812.53034)]. In the first section connections on almost symplectic manifolds are considered. Sections 2 and 3 are devoted to symplectic connections and their curvature properties. In the last two sections, the authors introduce normal coordinates on a Fedosov manifold and analyse the properties of the curvature tensor.
Reviewer: Dmitry Kalinin (Kazan’)

Cited in 4 Reviews
Cited in 59 Documents

MSC:

53D05 Symplectic manifolds (general theory)

Keywords:

symplectic connection; Fedosov manifold; curvature

Citations:

Zbl 0812.53034
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Full Text: DOI arXiv

References:

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