The fundamental form of a homogeneous Lagrangian in two independent variables

Details The fundamental form of a homogeneous Lagrangian in two independent variables The fundamental form of a homogeneous Lagrangian in two independent variables

2007-09-19

arxiv.org/abs/0709.3092v1

Mathematics

Differential Geometry

Scientific paper

We construct, for a homogeneous Lagrangian of arbitrary order in two
independent variables, a differential 2-form with the property that it is
closed precisely when the Lagrangian is null. This is similar to the property
of the `fundamental Lepage equivalent' associated with first-order Lagrangians
defined on jets of sections of a fibred manifold.

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