Painlevé analysis of the Ricci-flat ordinary differential equations associated with Aloff–Wallach spaces and U(1)-bundles over Fano products

We apply techniques of Painlevé–Kowalewski analysis to certain ODE reductions of the Ricci-flat equations. We particularly focus on two examples when the hypersurface is an Aloff–Wallach space or a circle bundle over a Fano product.