Möbius hypersurfaces in \(S^{n+1}\) with three distinct principal curvatures (Q1882453)

The author proves two theorems in Möbius geometry of hypersurfaces. In Theorem 1 he shows that a hypersurface in \(S^n\) with constant length of the second fundamental form is Euclidean isoparametric if and only if it is Möbius isoparametric. Theorem 2 states that a hypersurface with three Möbius principal curvatures is either Möbius isoparametric or Möbius isotropic if the eigenvalues of the Blaschke tensor are constant.