摘要
I. PREPARATION AND LEMMASWe start recalling theMain Theorem of Abresch. Given an isoparametric hypersurface in S<sup>n+1</sup> with g= 4, then the pair (m<sub>,</sub> m<sub>+</sub> )-w. r. g, we may assume that m<sub> </sub>≤m<sub>+</sub>, satisfies one of the three conditions below: