AdS non-linear curvature-squared and curvature-quartic multidimensional (D=8) gravitational models with stabilized extra dimensions

We investigate $D$-dimensional gravitational model with curvature-quadratic and curvature-quartic correction terms: $R+R^2+R^4$. It is assumed that the corresponding higher dimensional spacetime manifold undergos a spontaneous compactification to a manifold with warped product structure. Special attention is paid to the stability of the extra-dimensional factor space for a model with critical dimension D=8. It is shown that for certain parameter regions the model allows for a freezing stabilization of this space. The effective four-dimensional cosmological constant is negative and the external four-dimensional spacetime is asymptotically AdS.