Quasi-umbilical affine hypersurfaces congruent to their centre map
  In this paper, we study strictly convex affine hypersurfaces centroaffinely congruent to their centre map, in the case when the shape operator has two distinct eigenvalues: one of multiplicity 1, and one nonzero of multiplicity n-1. We show how to construct them from (n-1)-dimensional affine hyperspheres. 
A. J. Vanderwinden
math.DG