In this work, we use the formal definition of $k$-slant helix cite{ali2} to obtain the intrinsic equations as well as the position vector for emph{slant-slant helices} which a generalization of emph{general helices} and emph{slant helices}. Also, we present some characterizations theorems for $k$-slant helices and derived, in general form, the intrinsic equations for such curves. Thereafter, fr...

In this paper, we define X-slant helix in Euclidean 3-space and we obtain helix, slant helix, clad and g-clad helix as special case of the X-slant helix. Then we study Darboux, tangential darboux developable surfaces and their singular points. Especially we show that the striction lines of these surfaces are singular locus of the surfaces.

in this paper, biharmonic slant helices are studied according to bishop frame in the heisenberg group heis3. we give necessary and sufficient conditions for slant helices to be biharmonic. the biharmonic slant helices arecharacterized in terms of bishop frame in the heisenberg group heis3. we give some characterizations for tangent bishop spherical images of b-slant helix. additionally, we illu...

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.

We introduce the notion of a k-type slant helix in Minkowski space E1. For partially null and pseudo null curves in E1, we express some characterizations in terms of their curvature and torsion functions. AMS subject classifications: 53C40, 53C50

In this study, direction curves of spherical indicatrix (primarily tangent indicatrix) for a curve in three dimensional Euclidean space were investigated. Mentioned was given with new alternative frame which is {N,C,W} frame. It aspect that researching relations between and the main via The harmonic curvatures geodesic image principal normal obtained. general helix, slant helix C-slant characte...

In this work, the notion of a slant helix is extended to the space E. First, we introduce the type-2 harmonic curvatures of a regular curve. Thereafter, by using this, we present some necessary and sufficient conditions for a curve to be a slant helix in Euclidean n-space. We also express some integral characterizations of such curves in terms of the curvature functions. Finally, we give some c...

In this paper, we study slant helix using modified orthogonal frame in Minkowski space E31 with timelike, lightlike and spacelike axes. We also a general the Killing vector field axis. Furthermore, give non-trivial example find relations for curvature torsion of f-biharmonic helix.

Inclined curves or so-called general helices are well-known curves in the classical differential geometry of space curves [9] and we refer to the reader for recent works on this type of curves [6, 12]. Recently, Izumiya and Takeuchi have introduced the concept of slant helix in Euclidean 3-space E saying that the normal lines makes a constant angle with a fixed direction [7]. They characterize ...