  We construct the covariant or model independent induced Einstein-Yang-Mills
field equations on a 4-dimensional brane embedded isometrically in an
D-dimensional bulk space, assuming the matter fields are confined to the brane.
Applying this formalism to cosmology, we derive the generalized Friedmann
equations. We derive the density parameter of dark energy in terms of width of
the brane, normal curvature radii and the number of extra large dimensions. We
show that dark energy could actually be the manifestation of the local
extrinsic shape of the brane. It is shown that the predictions of this model
are in good agreement with observation if we consider an 11-dimensional bulk
space.
