Actions for Curved Branes
  The nondeterminantal forms of the Born-Infeld and related brane actions in which the gauge fields couple to both an induced metric and an intrinsic metric are generalised by letting either or both metrics be dynamical. The resulting actions describe ` brane world' and cosmological scenarios in which the gauge fields are confined to the brane, while gravity propagates in both the world-volume and the bulk. In particular, for actions involving a nonsymmetric ` metric', nonsymmetric gravity propagates on the worldvolume. For 3-branes with a symmetric metric, conformal (Weyl) gravity propagates on the worldvolume and has conformally invariant couplings to the gauge fields. 
Mohab Abou-Zeid