  We consider brane cosmology when the 4D Ricci scalar term is added to the 5D
Einstein-Hilbert action and discuss the role that the addition of this term has
on the brane-bulk system. The induced brane dynamics is shown to be the usual
Einstein dynamics coupled to a modified energy-momentum tensor which is well
defined once the 5D Einstein equations are solved in the bulk. The 5D Einstein
equations valid everywhere in the bulk, but not in the brane, are projected on
the brane. Then making use for the embedding of the brane in the bulk of the
Israel junction conditions, modified by a source term coming from the addition
of the intrinsic curvature scalar in the bulk action, it is possible to obtain
the effective 4D Einstein equations on the brane consistent with the bulk
geometry.
