Given a smooth bundle with a smooth manifold of dimension , then a horizontal -form on the jet bundle is a local Lagrangian. Its de Rham differential has a unique decomposition into a source form and a horizontally exact form (with respect to the variational bicomplex)
This source form is the Euler-Lagrange form of . It vanishes precisely at those points which are solutions to the Euler-Lagrange equations induced by .
The combination is the corresponding Lepage form.
Last revised on November 8, 2017 at 20:17:59. See the history of this page for a list of all contributions to it.