On hypersurfaces with parallel M¨obius form and constant para-Blaschke eigenvalues

Abstract

In this paper, we classify umbilic-free hypersurfaces of the unit sphere that have constant para-Blaschkeeigenvalues and possess parallel Mobius form. To achieve the classification, we first of all show that, under the conditionof having constant para-Blaschke eigenvalues, an umbilic-free hypersurface of the unit sphere is of parallel Mobius formif and only if its M¨obius form vanishes identically.