Classifying superpotentials: three summands case

TL;DR

This paper reviews previous classifications of superpotentials related to cohomogeneity one Ricci-flat equations and extends the classification to cases with exactly three irreducible summands in the isotropy representation.

Contribution

It provides a detailed classification of superpotentials for the specific case of three summands, completing the analysis from earlier works.

Findings

Classification of superpotentials with three summands completed

Extended understanding of scalar curvature type superpotentials

Clarified the structure of cohomogeneity one Ricci-flat equations

Abstract

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].