Ordinary diferantial equations and riemann structures

The aim of this thesis is to examine the curvature properties of manifolds, defined by first and second order ordinary differential equations, in terms of Riemannian geometry and the equivalent problem of differential equations, defined on Riemannian manifolds, is treated as the O(n, R)-valued equivalence problem formed by canonical contact forms representing equations and their equivalence classes constructed with the independence condition.For this purpose, first and second-order ordinary differential equations are res- pectively considered as manifolds within the jet spaces Riemannian metrics have been defined along with elements of exterior differential systems representing the equations within these manifolds.