Geodesic curves on quantized manifolds (Q1359687)

The authors apply the general definition of a linear connection in non-commutative geometry (proposed by A. Connes) to generalize the notion of geodesic curves on quantized manifolds. In the particular case of functional quantization, they define geodesics in the same way as in the classical case and show that the two definitions are compatible. They also examine the results obtained for the quantum Manin plane.