The cohomogeneity one Einstein equations and Painlevé analysis

We apply techniques of Painlevé–Kowalewski analysis to a Hamiltonian system arising from symmetry reduction of the Ricci-flat Einstein equations. In the case of doubly warped product metrics on a product of two Einstein manifolds over an interval, we show that the cases when the total dimension is 10 or 11 are singled out by our analysis.