In differential geometry, a Dupin hypersurface is a submanifold in a space form, whose principal curvatures have globally constant multiplicities.[1]
A hypersurface is called a Dupin hypersurface if the multiplicity of each principal curvature is constant on hypersurface and each principal curvature is constant along its associated principal directions.[2] All proper Dupin submanifolds arise as focal submanifolds of proper Dupin hypersurfaces.[3]