Classifying superpotentials: Three summands case

We give an overview of our classification results in Dancer and Wang (2005, 2008) [1] and [2] for superpotentials of scalar curvature type of the cohomogeneity one Ricci-flat equations. We then give an account of the classification in the case where the isotropy representation of the principal orbit consists of exactly three distinct irreducible real summands—the left over case from Dancer and Wang (2008) [2].