Superpotentials and the cohomogeneity one Einstein equations (Q818617)

The authors provide a detailed analysis of the existence of superpotentials in the Ricci-flat case. They successfully use some ideas from convex geometry to prove an interesting classification theorem under suitable hypotheses, for superpotentials of the Hamiltonian form of the cohomogeneity one Ricci-flat equations. Some new examples of superpotentials which do not satisfy the non-null hypothesis are given and their associated first order systems are analyzed. Superpotentials for the case when the cosmological constant is nonzero are briefly discussed as well.