Geodesic Curves on Quantized Manifolds
  A general definition of the curves and geodesics associated with a given connection on a quantized manifold is given. In the particular case of the functional quantization we define geodesics in the same way as in the classical case and we will show that the two definitions are compatible. As an example we examine our results for the quantum plane. 
V.Milani, A.Shafei Deh Abad