2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/183238We 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.12 pages, 2 figuresHigh Energy Physics - TheoryAstrophysicsGeneral Relativity and Quantum Cosmologytext