Spontaneous compactification with quadratic and cubic curvature terms

Certain curvature squared terms, which supplement the Einstein action in the low energy limit of string theories, allow for spontaneous compactification to Rsup((1,3)) x Ssup(n), n>=4. A cosmological constant in N=4+n dimensions is necessary. This is no longer the case if we add certain cubic curvature terms to the lagrangian. Solutions in N>=10 dimensions are obtained. The field equations considered contain at most second derivatives of the metric. (orig.)