Some characterizations of Mannheim partner curves in the Minkowski 3-space E13; pp. 210–220

Abstract

In this paper, we give some characterizations of Mannheim partner curves in the Minkowski 3-space E13. Firstly, we classify these curves in E13. Next, we give some relationships characterizing these curves and we show that the Mannheim theorem is not valid for the Mannheim partner curves in E13. Moreover, by considering the spherical indicatrix of the Frenet vectors of those curves, we obtain some new relationships between the curvatures and torsions of the Mannheim partner curves in E13.