  Starting with the Nambu-Goto action of the braneworld embedded in a curved
bulk, we derive the precise expressions for the quantum induced effects due to
small fluctuations of the brane. To define the brane fluctuations invariantly,
we introduce the Riemannian coordinate system for the subspace normal to the
braneworld. It will turn out that we can systematically incorporate the effects
of bulk curvature, and that the induced effects depend on the extrinsic
curvature and the normal-connection gauge field as well as on bulk curvature
components at the brane.
