Covariant gravitational equations on a brane world with a Gauss-Bonnet term

We present covariant gravitational equations to describe a four-dimensional brane world in the case with a Gauss-Bonnet term in a bulk spacetime, assuming that gravity is confined on the [Formula Presented] symmetric brane. It contains some components of the five-dimensional Weyl curvature [Formula Presented] which describes all effects from the bulk spacetime just as in the case of the Randall-Sundrum second model. Applying this formalism to cosmology, we derive the generalized Friedmann equation and calculate the Weyl curvature term, which is directly obtained from a black hole solution.