Classifying superpotentials: three summands case

We give an overview of our earlier classification results in [DW4] and [DW6] 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 leftover case from [DW6].