Developable normal surface pencil

Authors : Mustafa DEDE

Pages : 650-662

Doi:10.31801/cfsuasmas.1127781

View : 61 | Download : 48

Publication Date : 2023-09-30

Article Type : Research Paper

Abstract :In this paper, we introduce a new class of surfaces, called as normal surface pencil. We parameterize a normal surface pencil by using the principal normal vector $\\mathbf{n}$ and the binormal vector $\\mathbf{b}$ of the Frenet frame of a space curve $\\alphainsert ignore into journalissuearticles values(s);$ as follows $\\varphiinsert ignore into journalissuearticles values(s,t);=\\alphainsert ignore into journalissuearticles values(s);+yinsert ignore into journalissuearticles values(s,t);\\mathbf{n}+zinsert ignore into journalissuearticles values(s,t);\\mathbf{b}.$ A well known example of normal surface pencil is a canal surface. Finally, we propose the sufficient conditions of a normal surface pencil being a developable surface. Then several new examples of developable normal surface pencil are constructed from these conditions.
Keywords : Flat surfaces, Gauss curvature, surface pencil, developable