PARA-BLASCHKE ISOPARAMETRIC HYPERSURFACES IN THE UNIT SPHERE Sn+1(1) (II)

Let D = A + λB be the para-Blaschke tensor of the immersion x, where λ is a constant, A and B are the Blaschke tensor and the Möbius second fundamental form of x. A hypersurface x : M 7→ S(1) in the unit sphere S(1) without umbilical points is called a para-Blaschke isoparametric hypersurface if the Möbius form Φ vanishes identically and all of its para-Blaschke eigenvalues are constants. In [11], we classified the para-Blaschke isoparametric hypersurfaces with three distinct Blaschke eigenvalues, one of which is simple or with three distinct Möbius principal curvatures, one of which is simple. In this article, we continue to study the topic of para-Blaschke isoparametric hypersurfaces and obtain the classification of para-Blaschke isoparametric hypersurfaces with three distinct para-Blaschke eigenvalues, one of which is simple.