Dimensionally continued Euler forms: Kaluza-Klein cosmology and dimensional reduction

The most general gravity Lagrangian in more than four dimensions is considered which leads to field equations with at most second derivatives of the metric. It consists of a series of dimensionally continued Euler forms and allows spontaneous compactification. The field equations are elaborated for the usual Kaluza-Klein cosmology ansatz and solved in the special case where the extra dimensions form a sphere with constant radius. The dimensional reduction of the theory to four dimensions is discussed as well.