A novel approach to construct timelike developable surface with a common line of curvature

A. Çalışkan, Y. Ünlütürk, S. Kocabaş

Designing a timelike developable surface with a diagonalizable shape operator that has a non-null parametric curve as a line of curvature in three-dimensional Minkowski space is the issue that this study attempts to solve. A given curve on the surface is a timelike curvature line, a spacelike curvature line with a timelike normal vector, and a spacelike curvature line with a spacelike normal vector, respectively. According to these three different cases for the timelike developable surface, there are analyses in this work. In addition, investigations are carried out using the corresponding Darboux and Serret-Frenet frames for the timelike developable surface and the non-null line of curvature pair. The research outlines the prerequisites that must be met in order for the surface to be classified as a cylindrical surface (cylinder), conical surface (cone) or tangent surface. Additionally, examples with graphics are presented. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 17(2) (2024), pp. 137-156