  Assuming an Einstein-Gauss-Bonnet theory of gravitation in a ($D \geq
5$)-dimensional spacetime with boundary, we consider the problem of the
boundary dynamics given the matter Lagrangian on it. The resulting equation is
applied in particular on the derivation of the Friedmann eq. of a 3-brane,
understood as the non-orientable boundary of a 5d spacetime. We briefly discuss
the contradictory conclusions of the literature.
