Classification of hypersurfaces with parallel Laguerre second fundamental form in RnRn

Let x:M→Rnx:M→Rn be an umbilical free hypersurface with non-zero principal curvatures. Two basic invariants of x under the Laguerre transformation group are the Laguerre metric g   and the Laguerre second fundamental form BB. In this paper, we classify all oriented hypersurfaces in RnRn with a parallel Laguerre second fundamental form BB.