00982nas a2200121 4500008004100000245003800041210003800079260001500117490000600132520063500138100001700773856007000790 2000 eng d00aMetric Equivalence of Path Spaces0 aMetric Equivalence of Path Spaces c2000/01/010 v73 aLocal 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.1 aLackey, Brad uhttps://quics.umd.edu/publications/metric-equivalence-path-spaces