Stress-Energy-Momentum of Affine-Metric Gravity. Generalized Komar Superportential

In case of the Einstein's gravitation theory and its first order Palatini reformulation, the stress-energy-momentum of gravity has been proved to reduce to the Komar superpotential. We generalize this result to the affine-metric theory of gravity in case of general connections and arbitrary Lagrangian densities invariant under general covariant transformations. In this case, the stress-energy-momentum of gravity comes to the generalized Komar superpotential depending on a Lagrangian density in a precise way.Comment: 12 pp, LaTeX fil

Noether's second theorem in a general setting. Reducible gauge theories

We prove Noether's direct and inverse second theorems for Lagrangian systems on fiber bundles in the case of gauge symmetries depending on derivatives of dynamic variables of an arbitrary order. The appropriate notions of reducible gauge symmetries and Noether's identities are formulated, and their equivalence by means of certain intertwining operator is proved.Comment: 20 pages, to be published in J. Phys. A (2005

The Liouville-Arnold-Nekhoroshev theorem for non-compact invariant manifolds

Under ceratin conditions, generalized action-angle coordinates can be introduced near non-compact invariant manifolds of completely and partially integrable Hamiltonian systems.Comment: 8 page