The fundamental form of a second-order homogeneous Lagrangian in two variables

Details The fundamental form of a second-order homogeneous Lagrangian in two variables The fundamental form of a second-order homogeneous Lagrangian in two variables

2005-12-16

arxiv.org/abs/math/0512384v1

Mathematics

Differential Geometry

20 pages

Scientific paper

We construct, for a second-order homogeneous Lagrangian 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. We show that this form may be defined on a fourth-order frame bundle but is not, in general, projectable to a bundle of contact elements

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