Đề tài " Isoparametric hypersurfaces with four principal curvatures "

Let M be an isoparametric hypersurface in the sphere S n with four distinct principal curvatures. M¨nzner showed that the four principal curvatures can u have at most two distinct multiplicities m1 , m2 , and Stolz showed that the pair (m1 , m2 ) must either be (2, 2), (4, 5), or be equal to the multiplicities of an isoparametric hypersurface of FKM-type, constructed by Ferus, Karcher and M¨nzner from orthogonal representations of Clifford algebras. In this paper, u we prove that if the multiplicities satisfy m2 ≥ 2m1 − 1, then the isoparametric hypersurface M must be.

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