- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Cilt: 72 Sayı: 3
- Developable normal surface pencil
Developable normal surface pencil
Authors : Mustafa Dede
Pages : 650-662
Doi:10.31801/cfsuasmas.1127781
View : 37 | Download : 43
Publication Date : 2023-09-30
Article Type : Research
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 $\\alpha(s)$ as follows $\\varphi(s,t)=\\alpha(s)+y(s,t)\\mathbf{n}+z(s,t)\\mathbf{b}.$ 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