Euclidean Hypersurfaces with Genuine Conformal Deformations in Codimension Two

In this paper we classify Euclidean hypersurfaces f: Mⁿ→ Rⁿ⁺¹ with a principal curvature of multiplicity n- 2 that admit a genuine conformal deformation f~ : Mⁿ→ Rⁿ⁺². That f~ : Mⁿ→ Rⁿ⁺² is a genuine conformal deformation of f means that it is a conformal immersion for which there exists no open subset U⊂ Mⁿ such that the restriction f~ | _U is a composition f~|U=h∘f|U of f| _U with a conformal immersion h: V→ Rⁿ⁺² of an open subset V⊂ Rⁿ⁺¹ containing f(U).