Mannheim Curves In Non-flat 3-Dimensional Space Forms

In this paper, we consider the Mannheim curves in non-flat 3-dimensional space forms(Riemannian or Lorentzian) and we give the concept of Mannheim curves. In addition, weinvestigate the properties of non-null Mannheim curves and their partner curves. We cometo the conclusion that a necessary and sufficient condition is that a linear relationship withconstant coefficients shall exist between the curvature and the torsion of the given originalcurves. In the case of null curve, we reveal that there is no null Mannheim curve in the3-dimensional non-flat space.