notes on lifting of mannheim partner curve on tangent space t r3

In this paper, firstly, we define the mannheim partner curve of mannheim curve with respect to the vertical, complete and horizontal lifts on space r 3 to its tangent space t r3 = r 6 . secondly, we examine the frenet-serret aparatus {t ∗ (s), n∗ (s), b∗ (s), κ∗ (s), τ ∗ (s)} of the mannheim partner curve α ∗ according to the vertical, complete and horizontal lifts on t r3 by depend on the lifting of frenet-serret aparatus {t(s), n(s), b(s), κ(s), τ (s)} of the first curve α on space r 3 . in addition, we include all special cases the curvature κ ∗ (s) and torsion τ ∗ (s) of the frenet-serret aparatus of the mannheim partner curve α ∗ with respect to the vertical, complete and horizontal lifts on space r 3 to its tangent space t r3 . as a result of this transformation on space r 3 to its tangent space t r3 , we can speak about the features of mannheim partner curve of any curve on space t r3 by looking at the characteristics of the first curve α.