On the Trajectory Null Scrolls in 3-Dimensional Minkowski Space-Time E13

Abstract

Abstract. In this paper, the trajectory null scroll in 3-dimensional Minkowski space-timeE 31 is given by a firmly connected null oriented line moving with Cartan frame along nullcurve. Some theorems and results between curvatures of base curve and distribution pa-rameter of this surface are obtained. Moreover, some theorems and results related to beingdevelopable and minimal of this surface are given. And also, some relationships amonggeodesic curvature, geodesic torsion and the curvatures of null base curve of trajectorynull scroll are found. 1. IntroductionIn literature there are many studies related to ruled surfaces and their invari-ants (distribution parameters, Blaschke invariants, sectional curvature, apex angles,etc) in 3-dimensional Euclidean space E 3 , [1], [2]. In a spatial motion, the trajec-tories of oriented lines embedded in a moving space (or in a moving rigid body)are generally trajectory ruled surfaces (or ruled surfaces). Therefore the geometryof trajectory ruled surfaces is important in the study of space kinematics or spa-tial mechanisms. And also, the developable of the trajectory ruled surfaces havea number of applications in geometric modeling and model-based manufacturingof mechanical products, [3], [4], [5]. Lorentz metric in 3-dimensional Minkowskispace-time E