Affine hypersurfaces with self congruent center map

In this paper, we study locally strictly convex affine hypersurfaces for which the center map is centroaffine congruent with the original hypersurface. By the equiaffine support function rho, we show that the hypersurface is locally isometric to a warped product R x (root vertical bar rho vertical bar) N, where the gradient direction of rho is along R. As a main result, we complete the classification when grad rho is the eigenvector of affine shape operator, which shows how to explicitly construct such hypersurfaces starting from one (or two) low dimensional affine hypersphere(s). (C) 2015 Elsevier Inc. All rights reserved.