A class of cubic hypersurfaces and quaternionic K\"ahler manifolds of co-homogeneity one

Understand

We classify all complete projective special real manifolds with reducible cubic potential, obtaining four series.

• For two of the series the manifolds are homogeneous, for the two others the respective automorphism group acts with co-homogeneity one.
• Complete projective special real manifolds give rise to complete quaternionic K\"ahler manifolds via the supergravity q-map, which is the composition of the supergravity c-map and r-map.
• We develop curvature formulas for manifolds in the image of the q-map.