The second variation formula in Lagrange and Finsler geometry (Q2725480)

This paper presents a novel discussion of the general covariant second variation of arc length. This is applied to Finsler geometry where the second variation is shown to be independent of which of the four canonical connections (Cartan, Berwald, Chern-Rund, Hashiguchi) is chosen. This is closely related to a similar result of Bao and Chern where the flag curvature is also independent of the Finsler connection. The paper illustrates the usefulness of the general calculus of variations approach to Lagrange and Finsler geometry.