Metric Equivalence of Path Spaces

TitleMetric Equivalence of Path Spaces
Publication TypeJournal Article
Year of Publication2000
AuthorsLackey, B
JournalNonlinear Studies
Date Published2000/01/01

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.