3 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 $M\subset S^n$ be a compact proper Dupin hypersurface, meaning that it has constant multiplicities of its principal curvatures along each curvature surface. Two hypersurfaces a…

Let $M$ be a compact, connected proper Dupin hypersurface in $S^n$ with either four or six principal curvatures. Assume that its Lie curvatures are constant; these are the Lie-sphe…