%0 Journal Article %J Nonlinear Studies %D 2000 %T Metric Equivalence of Path Spaces %A Brad Lackey %X Local equivalence and the invariants of systems of second order differential equations were studied in a series of papers by Kosambi, Cartan, and Chern. The resulting theory, deemed KCC-theory, is a rich geometric study which in many ways generalizes Riemannian and Finsler geometry. Yet, in many applications one requires a metric structure in addition to the systems of second order differential equations. We pose a geometry which is equipped with both of these structures, and solve the problem of local equivalence and thus determining a preferred connection and finding a generating set for all the invariants of the theory. %B Nonlinear Studies %V 7 %8 2000/01/01 %G eng %N 2