Classification of complete Finsler manifolds through a second order differential equation

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.

💡 Research Summary

The paper introduces a novel method for classifying complete Finsler manifolds by exploiting a second‑order differential equation that plays a role analogous to the Obata equation in Riemannian geometry. The authors first define a “Finsler‑Obata” equation
\