The fundamental form of a homogeneous Lagrangian in two independent variables (Q1957173)

For a homogeneous Lagrangian of arbitrary order in two independent variables, a differential 2-form is constructed. This form is closed precisely when the Lagrangian is null. This property is similar to the ``fundamental Lepage equivalent'' associated with first-order Lagrangians defined on jets of sections of a fibred manifold. In sections 2--3, the properties of homogeneous variational problems are recalled in the context of a bicomplex of vector-valued forms. In sections 4--6, some preliminary results, the basic theorem of the work, and a discussion of some consequences of this result are presented.