Abstract
In this paper, we consider that Mannheim curve is timelike curve and Mannheim partner curve is timelike curve. Then, we investigate the relation between arc lengths and geodesic curvature of fixed pole curve ( ) C generated by Darboux vectorC with respect to Lorentz space 3 IL , Lorentz sphere 2 1 S or Hyperbolic sphere 2 0 H .In addition, we get, if the natural lifts geodesic spray of spherical indicator curvatures of Mannheim partner curve is an integral curve, then how Mannheim Curve is found to be. Mathematics Subject Classification: 53B30, 53C50
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