Timelike-spacelike Mannheım partner curves in IR31

Abstract

In this paper, timelike-spacelike Mannheim partner curve couple was defined in Lorentzian space 3 1 IR and the relations were given between the curvatures and torsions of these curves. Furthermore, for a given curve couple, the necassary and sufficient conditions were obtained to become timelikespacelike Mannheim partner curve couple in 3 1 IR .

The Spinor Expressions of Mannheim Curves in Euclidean 3-Space

“…where κ 1 and τ 1 are the curvatures of the Mannheim partner curve [20,31]. After these studies, many studies have been done on Mannheim curves [1,2,3,5,13,14,15,16,22,23,24,27].…”