We have derived a necessary and sufficient condition for non-null normal spacelike curve lying in or timelike surface M ⊂ E13, so that the becomes K-type slant helix with K ∈ {1,2,3}. used Darboux frame to define conditions. An example is given 1-type having binormal.

In this study, we consider framed curves as regular or singular space with an adapted frame in Euclidean 3-space. We define natural mates of a curve that are tangent to the generalized principal normal curve. Subsequently, present relationships between and its mates. particular, establish some necessary sufficient conditions for specific curves, such spherical helices, slant rectifying curves. ...

In classical differential geometry, the problem of the determination of the position vector of an arbitrary space curve according to the intrinsic equations κ = κ(s) and τ = τ (s) (where κ and τ are the curvature and torsion of the space curve ψ, respectively) is still open [7, 14]. However, in the case of a plane curve, helix and general helix, this problem is solved. In this paper, we solved ...

Abstract In this study, we define the generalized normal ruled surface of a curve in Euclidean 3-space E 3 . We study geometry such surfaces by calculating Gaussian and mean curvatures to determine when is flat or minimal (equivalently, helicoid). examine conditions for curves lying on be asymptotic curves, geodesics lines curvature. Finally, obtain Frenet vectors get some relations with helice...