On a class of polynomial Lagrangians

2001/11/09 by M. Palese, R. Vitolo
Physics and Astronomy · Mathematics · #math-ph #math.DG #math.MP #msc:58A20 #msc:58A12 #msc:58J10

paper · pdf

published as Rend.Circ.Mat.Palermo 66 (2001) 147-159 · LaTeX2e, amsmath, diagrams, hyperref; 15 pages

arxiv created 2001/11/09 · arxiv updated 2009/11/30

Abstract

In the framework of finite order variational sequences a new class of Lagrangians arises, namely, special Lagrangians. These Lagrangians are the horizontalization of forms on a jet space of lower order. We describe their properties together with properties of related objects, such as Poincaré--Cartan and Euler--Lagrange forms, momenta and momenta of generating forms, a new geometric object arising in variational sequences. Finally, we provide a simple but important example of special Lagrangian, namely the Hilbert--Einstein Lagrangian.

Related

• The Variational Sequence on Finite Jet Bundle Extensions and the Lagrangian Formalism
• The geometry of finite order jets of submanifolds and the variational formalism
• First-order equivalent to Einstein-Hilbert Lagrangian
• Nonlinear Lagrangians of the Ricci type
• Second-order Lagrangians admitting a first-order Hamiltonian formalism