On M(?)bius Form And M(?)bius Isoparametric Hypersurfaces

An umbilic-free hypersurface in the unit sphere is called M(o|¨)bius isoparametric if it satisfies two conditions, namely, it has vanishing M(o|¨)bius form and has constant M(o|¨)bius principal curvatures. In this paper, under the condition of having constant M(o|¨)bius principal curvatures, we show that the hypersurface is of vanishing M(o|¨)bius form if and only if its M(o|¨)bius form is parallel with respect to the Lcvi-Civita connection of its M(o|¨)bius metric. Moreover, typical examples are constructed to show that the condition of having constant M(o|¨)bius principal curvatures and that of having vanishing M(o|¨)bius form arc independent from each other.