f(R)-Einstein-Palatini Formalism and smooth branes

In this work, we present the f(R)-Einstein-Palatini formalism in arbitrary dimensions and the study of consistency applied to brane models, the so-called braneworld sum rules. We show that it is possible a scenario of thick branes in five dimensions with compact extra dimension in the framework of the f(R)-Einstein-Palatini theory by the accomplishment of an assertive criteria.