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, firstly, in $E_1^3$, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined fo...

A three dimensional model of the basic Helix-Loop-Helix motif and its sequence specific recognition of DNA is described. The basic-helix I is modeled as a continuous ?-helix because no ?-helix breaking residue is found between the basic region and the first helix. When the basic region of the two peptide monomers are aligned in the successive major groove of the cognate DNA, the hydrophobi...

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.

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 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 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.

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...