  By using a certain second order differential equation, the notion of adapted
coordinates on Finsler manifolds is defined and some classifications of
complete Finsler manifolds are found. Some examples of Finsler metrics, with
positive constant sectional curvature, not necessarily of Randers type nor
projectively flat, are found. This work generalizes some results in Riemannian
geometry and open up, a vast area of research on Finsler geometry.
