THE DIFFERENTIAL INVARIANTS
OF PARTICLE LAGRANGIANS UNDER EQUIVALENCE
BY CONTACT TRANSFORMATIONS

MICHAEL D. SUTTON

Abstract:

We use Élie Cartan's method of equivalence to derive the structure equations of the integral
under the group of contact transformations for the case m>1. These equations define a complete set of local differential invariants of the integral under contact transformations. We obtain a differential quadratic form and an associated system of frames which are intrinsic to and interpret our results from the standpoint of Finsler spaces. In the last section we explore some of the consequences of the structure equations.