In this paper, we give some characterizations of Mannheim partner curves in the Minkowski 3-space E¡. Firstly, we classify these curves in E^. Next, we give some relationships characterizing these curves and we show that the Mannheim theorem is not valid for the Mannheim partner curves in E¡. 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 E¡.

In this paper, we consider the idea of Bertrand partner curves for curves lying on surfaces and by considering the Darboux frames of surface curves, we call these curves as Bertrand partner D -curves and give the characterizations for these curves by means of the geodesic curvatures, the normal curvatures and the geodesic torsions of these associated curves.

In this paper, we give some characterizations for spacelike helices in Minkowski space-time E 4 1 . We find the differential equations characterizing the spacelike helices and also give the integral characterizations for these curves in Minkowski space-time E 4 1 .

Abstract. We introduce the notion of two-sided Γ-α-derivation of a Γ-near-ring and give some generalizations of [1,2].

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