Euclidean surfaces with conformal second fundamental form

Abstract

In the present study, we consider surfaces in E2+ d with conformal second fundamental form. We give a result for Chen surfaces to have a conformal second fundamental form. We show that every Chen surface is h-conformal. Furthermore, we give necessary and sufficient conditions for general rotational surfaces in Euclidean 4-space to become h-conformal. Finally, we prove that the Vranceanu surface is h-conformal if and only if it is either flat or minimal.