On the generalization of theorems from Riemannian to Finsler Geometry I: Metric Theorems

Details On the generalization of theorems from Riemannian to Finsler Geometry I: Metric Theorems On the generalization of theorems from Riemannian to Finsler Geometry I: Metric Theorems

2005-03-30

arxiv.org/abs/math/0503704v4

Mathematics

Differential Geometry

This paper has been withdrawn by the author

Scientific paper

A method to generalize results from Riemannian Geometry to Finsler geometry is presented. We use the method to generalize several results that involve only metric conditions. Between them we show that the topology induced by the Finsler structure is equivalent to the manifold topology, we provide a new proof of the Hopf-Rinow theorem in Finsler geometry and we prove the existence of the center of mass of a convex body when the non-symmetric distance function comes from a non-reversible Finsler function.

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