The same thing will be done with . In the presence of torsion, the connection is no longer equal to the Christoffel symbol. 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.
Thus, in conventional differential geometry it is not clear which of them should play a more fundamental role in physics. This postulate was made only for spaces with no torsion, in which case and are both symmetric. As mentioned in the Introduction, 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.