On simultaneous characterizations of partner-ruled surfaces in Minkowski 3-space

Abstract

In this study, the partner-ruled surfaces in Minkowski 3-space, which are defined according to the Frenet vectors of non-null space curves, are introduced with extra conditions that guarantee the existence of definite surface normals. First, the requirements of each pair of partner-ruled surfaces to be simultaneously developable and minimal (or maximal for spacelike surfaces) are investigated. The surfaces also simultaneously characterize the asymptotic, geodesic and curvature lines of the parameter curves of these surfaces. Finally, the study provides examples of timelike and spacelike partner-ruled surfaces and includes their graphs.

Keywords

• partner-ruled surface
• developable and minimal surface
• geodesic curve
• asymptotic curve