2 problems

Let $M$ be a compact, connected proper Dupin hypersurface in $S^n$, with $g$ distinct principal curvatures. The hypersurface has constant Lie curvatures when its Lie curvatures are…

Let $M$ be a compact, connected proper Dupin hypersurface in $S^n$ or ${\bf R}^n$. Cecil–Ryan conjecture. $M$ is Lie equivalent to an isoparametric hypersurface in $S^n$. The conje…