Riemannian Manifolds and Two of Hopf’s TheoremsA .. on a manifold . is a family of inner products {..}.∈. such that the quantities . are smooth in local coordinates. The Finsler function .(.) of a Riemannian manifold has the characteristic structure ..
Finsler Surfaces and a Generalized Gauss-Bonnet Theorems, we only use objects which are invariant under positive rescaling in .. Consequently, our treatment using natural coordinates on .