On the use of connections in the calculus of variations in Finsler geometry

Abstract

We propose a unified approach to the theory of connections in the geometry of sprays and Finsler metrics which, in particular, gives a simple explanation of the well-known fact that all the classical Finslerian connections provide exactly the same formulas appearing in the calculus of variations.

arXiv comment14 pages. Title changed. To appear in the Bulletin of the Brazilian Mathematical Society