The procedure to find gauge invariant variables for two-parameter nonlinear perturbations in general relativity is considered. Up to third order perturbations, it is shown that appropriate combinations of nonlinear metric perturbations and lower order one are transformed as the gauge transformation of linear order metric perturbations. This implies that gauge invariant variables for the higher ...

We consider an invariant skew-symmetric phase-space metric for nonHamiltonian systems. We say that the metric is an invariant if the metric tensor field is an integral of motion. We derive the time-dependent skewsymmetric phase-space metric that satisfies the Jacobi identity. The example of non-Hamiltonian systems with linear friction term is considered. PACS numbers: 45.20.−d, 02.40.Yy, 05.20.−y

The spectral metric, defined by Schwarz and Oh using Floertheoretical method, is a bi-invariant metric on the Hamiltonian diffeomorphism group. We show in this note that for certain symplectic manifolds, this metric can not be extended to a bi-invariant metric on the full group of symplectomorphisms. We also study the bounded isometry conjecture of Lalonde and Polterovich in the context of the ...