Consistency of Higher Derivative Gravity in the Brane Background

We consider the theory of higher derivative gravity with non-factorizable Randall-Sundrum type space-time and obtain the metric solutions which characterize the $p$-brane world-volume as a curved or planar defect embedded in the higher dimensions. We consider the string inspired effective actions of the dilatonic Gauss-Bonnet type in the brane background and show its consistency with the RS brane-world scenario and the conformal weight of the dilaton couplings in the string theory with apppropriate choice of Regge slope (${\alpha }^{\mathrm{\prime }}$) or Gauss-Bonnet coupling ($\alpha$) or both. We also discuss a time dependent dilaton solution for a string-inspired fourth-derivative gravity.