On the Geometric Structure of Hypersurfaces of Conullity Two in Euclidean Space

Abstract

In this paper we introduce the notion of a semi-developable surface of codimension two as a generalization of the notion of a developable surface of codimension two. We give a characterization of the developable and semi-developable surfaces in terms of their second fundamental forms. We prove that any hypersurface of conullity two in Euclidean space is locally a foliation of developable or semi-developable surfaces of codimension two.