Since the two types of lines play geometrically an equally favored role, the question arises as to which of them describes the correct classical particle orbits. The answer will be given at the end of this section. In the last term we have used a matrix notation for the connection. In the last term, the 's are viewed as matrices . The symbols denote the covariant derivatives formed with the Christoffel symbol.
Covariant derivatives act like ordinary derivatives if they are applied to a scalar field.
This will be of use later. This postulate was made only for spaces with no torsion, in which case and are both symmetric. As mentioned before, it is not yet clear how Einstein's field equations should be generalized in the presence of torsion since the experimental consequences are as yet too small to be observed. In this paper, we are not concerned with the generation of curvature and torsion but only with their consequences upon the motion of point particles. Two nonholonomic sample mappings producing curvature and torsion are shown in Fig.