New pencils of biharmonic helices via the application of developable surfaces in Heisenberg groups

Abstract

In this article, we introduce the concept of pencil surfaces via biharmonic slant helix as indicated by Bishop frame in Heisenberg groups. Pencil surfaces are expressed by biharmonic B-slant helix Bishop frame in Heisenberg group. Furthermore, we give some new necessary and sufficient conditions for pencil surfaces. Finally, our theoretical results are illustrated by graphical representations of B-pencil surfaces.