Hypersurfaces with Two Distinct Para-Blaschke Eigenvalues inSn+1(1)

Let x:M↦Sn+1(1) be an n  (n≥3)-dimensional immersed hypersurface without umbilical points and with vanishing Möbius form in a unit sphere Sn+1(1), and let A and B be the Blaschke tensor and the Möbius second fundamental form of x, respectively. We define a symmetric (0,2) tensor D=A+λB which is called the para-Blaschke tensor of x, where λ is a constant. An eigenvalue of the para-Blaschke tensor is called a para-Blaschke eigenvalue of x. The aim of this paper is to classify the oriented hypersurfaces in Sn+1(1) with two distinct para-Blaschke eigenvalues under some rigidity conditions