In this paper, we study spinor Bishop equations of curves in 3 . We research the spinor formulations of curves according to Bishop frames in 3 . Also, the relation between spinor formulations of Bishop frames and Frenet frame are expressed.

In this study, sliding velocity, pole lines, hodograph, and acceleration poles of two-parameter Lorentzian homothetic motions at ∀(λ, μ) positions are obtained. By defining two-parameter Lorentzian homothetic motion along a curve in Lorentzian space L 3 , the theorems related to this motion and characterizations of the trajectory surface are given.

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In this study, spinor representations of the curves on surfaces have been expressed via B-Darboux frame in Euclidean space E^3. The relation between Darboux and B-Darboux frame has been established according to their spinor formulations. Moreover, all these spinor characterizations have been interpreted in the meaning of Darboux frame (via the curvatures) in Euclidean 3-space. Finally, an application has been presented about the characterizations of the relations between the B-Darboux frame and the spinors.

In this study, Rodrigues parameters have been first calculated for a homothetic rotation around spacelike and timelike axis using one parameter homothetic motions in Lorentz 3-space E 1 3 ${\mathbb{E}}_{1}^{3}$ . The behavior of the vectors during the homothetic rotation, which is the increase or decrease (about size of one of the objects in motion) notion, has been investigated as a three dimensional shape with the help of Cinema 4D program. The behavioral differences have been observed on figures. Then, Lorentz motions that corresponding to the homothetic rotation matrices in terms of spacelike and timelike axes have been examined and expressed in E 1 3 ${\mathbb{E}}_{1}^{3}$ . Some definitions, theorems, corollaries and three dimensional figures have been given in Lorentz 3-space.