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Fedosov manifolds. (English) Zbl 0945.53047
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.

MSC:
53D05 Symplectic manifolds (general theory)
Citations:
Zbl 0812.53034
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