Related papers: New special curves and their spherical indicatrice…

In this paper, we find all constant slope surfaces in the Euclidean 3-space, namely those surfaces for which the position vector of a point of the surface makes constant angle with the normal at the surface in that point. These surfaces…

Special curves and their characterizations are one of the main area of mathematicians and physicians. As a special curve we will mainly focus on Mannheim curve which has the following relation: k1={\beta}(k1^2+k2^) where k1 and k2 are…

In this study, we give definitions and characterizations of eikonal slant helices, eikonal Darboux helices and non-normed eikonal Darboux helices in 3-dimensional pseudo- Riemannian manifold M . We show that every eikonal slant helix is…

Here we introduce the concept of special effect curve which permits to study, from a different point of view, special linear systems in P^2, i.e. linear system with general multiple base points whose effective dimension is strictly greater…

In this study, we give definitions and characterizations of eikonal slant helix curves, eikonal Darboux helices and non-normed eikonal Darboux helices in three dimensional Riemannian manifold 3 M . We show that every eikonal slant helix is…

In this paper, we study the position vectors of rectifying slant helices in $E^3$. First, we have found the general equations of the curvature and the torsion of rectifying slant helices. After that, we have constructed a second order…

In this paper, we give the defination of harmonic curvature function some special curves such as helix, slant curves, Mannheim curves and Bertrand curves. Then, we recall the characterizations of helices [8], slant curves (see [19]) and…

In this paper we consider the idea of Bertrand curves for curves lying on surfaces and by considering the Darboux frames of them we define these curves as Bertrand D-curves and give the characterizations for these curves. We also find the…

A novel formulation of the Lie-Darboux method of obtaining the Riccati equations for the spatial curves in Euclidean three-dimensional space is presented. It leads to two Riccati equations that differ by the sign of torsion. The case of…

We propose a notion of discrete elastic and area-constrained elastic curves in 2-dimensional space forms. Our definition extends the well-known discrete Euclidean curvature equation to space forms and reflects various geometric properties…

We consider the curves whose all normal planes are at the same distance from a fixed point and obtain some characterizations of them in the 3-dimensional Euclidean space.

In this paper we provide a characterization for a class of convex curves on the 3-sphere. More precisely, using a theorem that decomposes a locally convex curve on the 3-sphere as a pair of curves on the 2-sphere, one of which is locally…

In this paper, we introduce the notion of an anti-torqued slant helix in a Riemannian manifold, defined as a curve whose principal vector field makes a constant angle with an anti-torqued vector field globally defined on the ambient…

In this work, we study plane and spherical curves in Euclidean and Lorentz-Minkowski 3-spaces by employing rotation minimizing (RM) frames. By conveniently writing the curvature and torsion for a curve on a sphere, we show how to find the…

The aim of this paper is to give some characterizations for N-Legendre and N-slant curves in the unit tangent bundles of surfaces endowed with natural diagonal lifted structures.

We introduce semi-helix hyper surfaces of Euclidean spaces. We also provide a local characterization of how these semi-helices are constructed.

In this paper, we define slant helices in three dimensional Lie Groups with a bi-invariant metric and obtain a characterization of slant helices. Moreover, we give some relations between slant helices and their involutes, spherical images.

In this paper, we give definitions and characterizations of normal and spherical curves in the dual space. We show that normal curves are also spherical curves in D^3.

In this paper, we study strong r-helix hypersurfaces and the special curves on these surfaces. Moreover, we investigated the relations between strong r-helix hypersurfaces and the Gauss transformations of these surfaces in Euclidean…

We prove that general helices in Euclidean space for Killing vector fields associated to rotations are helices, that is, curves with constant curvature and constant torsion. In hyperbolic space $\h^3$, we obtain the parametrization of…