On null Lagrangians (Q1775931)

This paper organizes some important results in the theory of homogeneous Lagrangians. One can construct a canonical Lagrangian form which is closed exactly when the Lagrangian is null. In the case of first-order homogeneity the variation integrals are parameter-independent, and the use of special (affine) coordinates leads to the result that the Carathéodory form and the fundamental Lepage equivalent are identical.