In this paper, the curvature and torsion of Smarandache curves obtained by vectors Bertrand partner curve are calculated. These values expressed depending upon curve. Besides, we illustrate example with our main results.

In this study, sufficient conditions are derived and examples created to derive surfaces with constant Gauss curvature along a given curve in terms of the linear combination its Frenet frame 3-dimensional Lie group.

With the help of the Frenet frame of a given pseudo null curve, a family of parametric surfaces is expressed as a linear combination of this frame. The necessary and sufficient conditions are examined for that curve to be an isoparametric and asymptotic on the parametric surface. It is shown that there is not any cylindrical and developable ruled surface as a parametric surface. Also, some inte...

abstract: In this paper, we analyzed the problem of consructing a family of surfaces from a given some special Smarandache curves in Euclidean 3-space. Using the Frenet frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary and sufficient conditions for coefficents to satisfy both the asymptoti...

We define normal curves in Minkowski space-time E4 1 . In particular, we characterize the spacelike normal curves in E4 1 whose Frenet frame contains only non-null vector fields, as well as the timelike normal curves in E4 1 , in terms of their curvature functions. Moreover, we obtain an explicit equation of such normal curves with constant curvatures.

In this paper, using pseudo-spherical Frenet frame of pseudospherical curves in hyperbolic space, we define the notion of the structure functions on the non-developable ruled surfaces with timelike ruling. Then we obtain the properties of the structure functions and a complete classification of the non-developable ruled surfaces with timelike ruling in Minkowski 3-space by the theories of the s...

An orthonormal frame (f1, f2, f3) is rotation–minimizing with respect to fi if its angular velocity ω satisfies ω · fi ≡ 0 or, equivalently, the derivatives of fj , fk are both parallel to fi. The Frenet frame (t,p,b) is rotation–minimizing with respect to the principal normal p, and in recent years adapted frames that are rotation–minimizing with respect to the tangent t have attracted much in...

In this paper, hyperbolic spinor representations of space curves are studied according to the q-frame in E_1^3. The formulations calculated for spacelike and timelike tangent vector cases Moreover, relationships equations between Frenet frame Lorentz expressed. results supported with some theorems.

In this study, a kind of generalized involute and evolute curve pair is considered in 4 dimensional semi Euclidean space with 2 index. The curvatures the associated Frenet Frame generalized
 involute-evolute are presented.