Path structures on manifolds

We study collections of paths—i.e., unparametrized curves—on a manifold such that through every point and every direction at that point there passes exactly one path. Among such path structures we characterize, analytically and in terms of symmetries, those which consist of geodesics of a linear connection. Examples of nongeodesic path structures are given, and some of the results are interpreted physically. Journal of Mathematical Physics is copyrighted by The American Institute of Physics