On a Connection Used in Deformation Quantization

Using natural lifting operations, we give a coordinate-free proof of the fact that connection used by Bordemann, Neumaier and Waldmann to construct Fedosov standard ordered star product on cotangent bundle Riemannian manifold is obtained symplectification complete lift corresponding Levi-Civita connection, in sense Yano Patterson. In terms local coordinates, this has already been shown Plebanski, Przanowski Turrubiates.