Laguerre isopararmetric hypersurfaces in .4

Let x: M . .n be an umbilical free hypersurface with non-zero principal curvatures. Then x is associated with a Laguerre metric g, a Laguerre tensor L, a Laguerre form C, and a Laguerre second fundamental form B which are invariants of x under Laguerre transformation group. A hypersurface x is called Laguerre isoparametric if its Laguerre form vanishes and the eigenvalues of B are constant. In this paper, we classify all Laguerre isoparametric hypersurfaces in .4.