Classification of the Blaschke Isoparametric Hypersurfaces with Three Distinct Blaschke Eigenvalues

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An immersed umbilic-free submanifold in the unit sphere is called Blaschke isoparametric if its Mobius form vanishes identically and all of its Blaschke eigenvalues are constant. Then the classification of Blaschke isoparametric hypersurfaces is natural and interesting in the Mobius geometry of submanifolds. In this paper, we give a classification of the Blaschke isoparametric hypersurfaces with three distinct Blaschke eigenvalues one of which is simple.