Fedosov manifolds (Q1269469)

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 \textit{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.