We extend our previous classification [DW4] of superpotentials of "scalar curvature type" for the cohomogeneity one Ricci-flat equations. We now consider the case not covered in [DW4], i.e., when some weight vector of the superpotential lies outside ...

Document(s)

Title

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...

We apply Painlevé analysis to the Ricci-flat Einstein equations for a warped product with an arbitrary number of factors. We find that, as in the situation of the two factors examined [J. Geom. Phys. 38, 183-206 (2001)], the cases when the total dime...

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. © 2003 American I...

Using ideas from convex geometry, we prove a classification theorem, under suitable hypotheses, for superpotentials of the Hamiltonian form of the cohomogeneity one Ricci-flat equations. Some new superpotentials are also constructed and their associa...

We produce explicit solutions for some cases of the cohomogeneity one Einstein equations by finding generalised first integrals of the Hamiltonian form of these equations. The resulting manifolds have dimension 10, 11 and 27.