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

Abstract

Letx:M↦Sn+1(1)be ann  (n≥3)-dimensional immersed hypersurface without umbilical points and with vanishing Möbius form in a unit sphereSn+1(1), and letAandBbe the Blaschke tensor and the Möbius second fundamental form ofx, respectively. We define a symmetric(0,2)tensorD=A+λBwhich is called the para-Blaschke tensor ofx, whereλis a constant. An eigenvalue of the para-Blaschke tensor is calleda para-Blaschke eigenvalueofx. The aim of this paper is to classify the oriented hypersurfaces inSn+1(1)with two distinct para-Blaschke eigenvalues under some rigidity conditions.