Abstract:In this paper, Frenet vector fields, curvature and torsion of the natural lift curve of a given curve is calculated by using the angle between Darboux vector field and the binormal vector field of the given curve in . Also, a similar calculation is made in considering timelike or spacelike Darboux vector field.

In this article, firstly, the isomorphism between the subset of the tangent bundle of Lorentzian unit sphere, TM, and Lorentzian unit sphere, S12 is represented. Secondly, the isomorphism between the subset of hyperbolic unit sphere, TM, and hyperbolic unit sphere, H2 is given. According to E. Study mapping, any curve on S12 or H2 corresponds to a ruled surface in R13. By constructing these isomorphisms, we correspond to any natural lift curve on TM or TM a unique ruled surface in R13. Then we calculate striction curve, shape operator, Gaussian curvature and mean curvature of these ruled surfaces. We give developability condition of these ruled surfaces. Finally, we give examples to support the main results.

Highlights• A unique ruled surface is corresponded to the natural lift curve.• Properties of ruled surfaces generated by natural lift curves are examined. • A method is given for modelling motions on ̅ instead of 2 .

In this paper, we study the spherical indicatrices of involutes of a spacelike curve with spacelike binormal. Then we give some important relationships between arc lengths and geodesic curvatures of the spherical indicatrices of involute-evolute curve couple in Minkowski 3-space. Also, we give some important results about curve couple.

Abstract. In this paper, we compute the Frenet vectors and the curvatures of the spacelike intersection curve of three spacelike hypersurfaces given by their parametric equations in four-dimensional Minkowski space E 4 1 . Introduction.The surface-surface intersection(SSI) is one of the basic problems in computational geometry. The main purpose here is to determine the intersection curve between the surfaces and to get information about the geometrical properties of the curve. Since the surfaces are mostly given by their parametric or implicit equations, three cases are valid for the SSI problems: parametric-parametric, implicit-implicit and parametricimplicit.There are two types of SSI problems: transversal or tangential. The intersection at the intersecting points is called transversal if the normal vectors of the surfaces are linearly independent, and is called tangential if the normal vectors of the surfaces are linearly dependent. The tangent vector of the intersection curve can be obtained easily by the vector product of the normal vectors of the surfaces in transversal intersection problems. Therefore, so many studies have recently been done about this type of problems. Hartmann [6], provides formulas for computing the curvatures of the intersection curves for all types of intersection problems in three-dimensional Euclidean space. Willmore [11], and using the implicit function theorem