Classification of complete Finsler manifolds through a second order differential equation

Details Classification of complete Finsler manifolds through a second order differential equation Classification of complete Finsler manifolds through a second order differential equation

2007-10-15

arxiv.org/abs/0710.2616v1

Differential Geometry and its Applications 26 (2008) 434--444

Mathematics

Differential Geometry

Scientific paper

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.

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