2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/213757We review some recent results obtained from the application of the Gauss-Codazzi formalism to brane-worlds models in the Brans-Dicke gravity. The cases of 4-branes embedded in a six-dimensional with and without $\mathbb{Z}_{2}$ symmetry are both analyzed.10 pages. Invited contribution to the Special Issue "The Problems of Modern Cosmology", on the occasion of Prof. S. D. Odintsov's 50th birthdayGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theorytext