Under assumptions on principal curvatures and constant S, f3, f4, closed minimal hypersurfaces M^5 in S^6 are isoparametric; those with a point of exactly two distinct principal curvatures are Clifford tori.
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Minimal Hypersurfaces with constant scalar curvature in $\mathbf{S}^6$
Under assumptions on principal curvatures and constant S, f3, f4, closed minimal hypersurfaces M^5 in S^6 are isoparametric; those with a point of exactly two distinct principal curvatures are Clifford tori.