A variational setting for an indefinite Lagrangian with an affine Noether charge

Abstract

We introduce a variational setting for the action functional of an autonomous and indefinite Lagrangian on a finite dimensional manifold. Our basic assumption is the existence of an infinitesimal symmetry whose Noether charge is the sum of a one-form and a function. Our setting includes different types of Lorentz-Finsler Lagrangians admitting a timelike Killing vector field.

42 pages, AMSLaTeX. v2: some small mistakes corrected in Examples 3.4,3.6, 3.9 and at the end of the proof of Prop. A1

References in corpus (5)

• Light cones in Finsler spacetime
• Foundations of Finsler spacetimes from the Observers' Viewpoint
• Routh's procedure for non-Abelian symmetry groups
• Redshift in Finsler spacetimes
• On the analyticity of static solutions of a field equation in Finsler gravity

Cited by in corpus (1)

• Fixed energy solutions to the Euler-Lagrange equations of an indefinite Lagrangian with affine Noether charge