In this paper, we introduce new adjoint curves which are associated in Euclidean space of three dimension. They generated with the help integral special Smarandache curves. We attain some connections between Frenet apparatus these and main curve. characterize conditions they general helix slant helix. Finally, exemplify them figures.

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 ...

In this paper, we analyse the proper curve $\gamma(s)$ lying on pseudo-sphere. We develop an orthogonal frame $\lbrace V_{1}, V_{2}, V_{3} \rbrace$ along curve, pseudosphere. Next, find condition for to become $V_{k} -$ slant helix in Minkowski space. Moreover, another $\beta(\bar{s})$ pseudosphere or hyperbolic plane heaving $V_{2} = \bar{V_{2}}$ which \bar{V_{1}},\bar{V_{2}},\bar{V_{3}} \rbra...

In the present work, we have dealt with properties of associated curves a Frenet curve in R14. addition to this, define principal direction curve, B_1 -direction B_2- given by using integral 4-dimensional Minkowski space. Then introduce some characterizations for general helix and slant helix. Finally, new theorems obtained space-like time- like Also, an example is given.

We consider a curve α = α(s) in Minkowski 3-space E31 and denote by {T,N,B} the Frenet frame of α. We say that α is a slant helix if there exists a fixed direction U of E31 such that the function 〈N(s), U〉 is constant. In this work we give characterizations of slant helices in terms of the curvature and torsion of α. MSC: 53C40, 53C50

By using the Darboux frame |?, ?, ?| of a non-null curve lying on timelike surface in Minkowski 3-space, where ? is unit tangent vector curve, spacelike normal field restricted to and = ?? we define relatively normal-slant helices as curves satisfying condition that scalar product fixed spanning their axis non-constant constant. We give necessary sufficient conditions for be helices. consider s...

In this work, we deal with a classical differential geometry topic in Minkowski space-time. First, we prove that there are no timelike involutes of a time-like evolute. In the light of this result, we observed that involute curve transforms to a time-like curve when evolute is a space-like helix with a time-like principal normal. Then, we investigated relationships among Frenet-Serret apparatus...