Ruled surfaces of finite type with respect to the second fundamental form

Abstract

In this article, we consider surfaces in the 3-dimensional Euclidean space E3 without parabolic points which are of finite II-type, that is, they are of finite type, in the sense of B.-Y. Chen, corresponding to the second fundamental form. We study an important family of surfaces, namely, ruled surfaces in E3. We show that ruled surfaces are of infinite II-type.