Laguerre isoparametric hypersurfaces in R super(n) with two distinct non-zero principal curvatures

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).An umbilical free oriented hypersurface x: M arrow right R super(n) with non-zero principal curvatures is called a Laguerre isoparametric hypersurface if its Laguerre form ... vanishes and Laguerre shape operator ... has constant eigenvalues. Here rho = capital sigma sub(i) (r - r sub(i)) super(2), ... is the mean curvature radius and S is the shape operator of x. {E sub(i)} is a local basis for Laguerre metric g = sigma super(2)III with dual basis { omega sub(i)} and III is the third fundamental form of x. In this paper, we classify all Laguerre isoparametric hypersurfaces in R super(n) (n > 3) with two distinct non-zero principal curvatures up to Laguerre transformations.