Asymptotical AdS space from nonlinear gravitational models with stabilized extra dimensions

We consider nonlinear gravitational models with a multidimensional warped product geometry. Particular attention is payed to models with quadratic scalar curvature terms. It is shown that for certain parameter ranges, the extra dimensions are stabilized if the internal spaces have a negative constant curvature. In this case, the four-dimensional effective cosmological constant as well as the bulk cosmological constant become negative. As a consequence, the homogeneous and isotropic external space is asymptotically ${\mathrm{AdS}}_4.$ The connection between the D-dimensional and the four-dimensional fundamental mass scales sets a restriction on the parameters of the considered nonlinear models.