  We show how the gravity, gauge, and matter fields are induced on dynamically
localized brane world (domain wall, vortex etc.). Solitonic solutions localized
on a curved brane in certain field theories in higher dimensions are given in
terms of gravity, gauge and extrinsic curvature fields of the brane. Then we
deduce the effective field theory on the brane in terms of those fields and the
quantum fluctuations of the solitonic solution. The gravity, gauge and the
extrinsic curvature fields should obey the Gauss-Codazzi-Ricci equation in
addition to their own equations of motion.
