Collineations in Path-Space

Curves representing solutions of (1) can be regarded as the generalized autoparallel lines or paths of a space, and the intrinsic differential geometry thereof is developed from two main assumptions: (a) the tensor invariance of all fundamental equations, including (1), and (b) the existence of a vectorial operator, the vanishing of which defines a parallelism making solutions of (1) autoparallel lines.