Conserved currents in $D$-dimensional gravity and brane cosmology

In $D$-dimentional gravity on arbitrary curved backgrounds using proven methods conserved currents, divergences of antisymmetrical tensor densities (superpotentials), are constructed. These superpotentials have two remarkable properties: they depend in an essential way on second derivatives in the Lagrangian and are independent on divergences added to it. The conserved currents are thus particulary well adapted to the case of perturbations in Gauss-Bonett cosmological brane theories.