We investigate the ruled surfaces generated by a straight line in Bishop frame moving along a spacelike curve in Minkowski 3-space. We obtain the distribution parameters, mean curvatures. We give some results and theorems related to be developable and minimal of them. Furthermore, we show that, if the base curve of the ruled surface is also an asymtotic curve and striction line, then the ruled surface is developable.

In this paper, we study ruled surface in 3-dimensional almost contact metric manifolds by using surface theory defined by Gök [Surfaces theory in contact geometry, PhD thesis (2010)]. We also studied the theory of curves using cross product defined by Camcı. In this study, we obtain the distribution parameters of the ruled surface and then some results and theorems are presented with special cases. Moreover, some relationships among asymptotic curve and striction line of the base curve of the ruled surface have been found.

In the present paper, the geometrical instantaneous invariants of the motion H m /H f in dual Lorentzian 3 -space are determined. Depending on this, the dual Lorentzian instantaneous screw axis of the motion of K m with respect to the dual pseudohyperbolic space K m is constructed. On the other hand, we show that, in each position of H m , the fixed and moving axodes have the instantaneous screw axis of this position in common. We also give relations between the geodetic curvature and the curvature of the polodes.

In this paper, we focus on the theory of the ruled surfaces with respect to type-2 Bishop frame. Firstly, type-2 Bishop motion is defined for space curve and then Darboux vector of this motion is calculated for fixed and moving spaces in E 3. We obtained the distribution parameter of a ruled surfaces generated by a darboux vector in type-2 Bishop trihedron moving along a curve and we show that the ruled surfaces whose generated by a darboux vector is developable but according to the type-2 Bishop frame, there is no developable ruled surfaces generated by the straight line in type-2 Bishop trihedron moving along a curve.

<abstract><p>If both the arc length and the intrinsic curvature of a curve or surface are preserved, then the flow of the curve or surface is said to be inextensible. The absence of motion-induced strain energy is the physical characteristic of inextensible curve and surface flows. In this paper, we study inextensible tangential, normal and binormal ruled surfaces generated by a curve with constant torsion, which is also called a Salkowski curve. We investigate whether or not these surfaces are minimal or can be developed. In addition, we prove some theorems which are related to inextensible ruled surfaces within three-dimensional Euclidean space.</p></abstract>