On the Maslov index in a symplectic reduction and applications

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

“…The Lagrangians that we consider (see Section 3) include, but are not limited to, C 1 stationary Lorentzian metrics, electromagnetic type Lagrangians on a stationary Lorentzian manifold with a Killing vector field K and K-invariant potentials (see, e.g. [6,16,19,50]) and some stationary Lorentz-Finsler metrics. Loosing speaking, a Lorentz-Finsler metric is an indefinite, positively homogeneous of degree two in the velocities, Lagrangian that generalizes the quadratic form of a Lorentzian metric in the same way as the square of a Finsler metric generalizes the square of the norm of a Riemannian metric.…”

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

“…3) include, but are not limited to, C 1 stationary Lorentzian metrics, electromagnetic type Lagrangians on a stationary Lorentzian manifold with a Killing vector field K and K -invariant potentials (see, e.g. [6,16,19,50]) and some stationary Lorentz-Finsler metrics. Loosing speaking, a Lorentz-Finsler metric is an indefinite, positively homogeneous of degree two in the velocities, Lagrangian that generalizes the quadratic form of a Lorentzian metric in the same way as the square of a Finsler metric generalizes the square of the norm of a Riemannian metric.…”