Related papers: On a new type Bertrand curve
In this study, we define a new type of direction curves in the Euclidean 3-space such as osculating-direction curve. We give the characterizations for these curves. Moreover, we obtain the relationships between osculating direction curves…
This paper describes the foundations of a differential geometry of a quaternionic curves. The Frenet-Serret equations and the evolutes and evolvents of a particular quaternionic curve are accordingly determined. This new formulation takes…
In this paper, it is proved that, no special timelike Frenet curve is a Bertrand curve in $\mathbb{E}_2^4$ and also, in $\mathbb{E}_\nu^{n+1}$ $ ({n \ge 3})$, such that the notion of Bertrand curve is definite only in $\mathbb{E}_1^2$ and…
We give a combinatorial description of closed curves on oriented surfaces in terms of certain permutations, called charts. We describe automorphisms of curves in terms of charts and compute the total number of curves counted with…
In this paper, we define a new family of curves and call it a {\it family of similar curves with variable transformation} or briefly {\it SA-curves}. Also we introduce some characterizations of this family and we give some theorems. This…
In this work, first, we express some characterizations of helices and ccr curves in the Euclidean 4-space. Thereafter, relations among Frenet-Serret invariants of Bertrand curve of a helix are presented. Moreover, in the same space, some…
In this paper, we consider a regular curve on an oriented surface in Euclidean 3-space with the Darboux frame $\{\mathsf{T},\mathsf{V},\mathsf{U}\}$ along the curve, where $\mathsf{T}$ is the unit tangent vector field of the curve,…
In this paper, tangent-, principal normal-, and binormal-wise associated curves are defined such that each of these vectors of any given curve lies on the osculating, normal, and rectifying plane of its mate, respectively. For each…
In the article, we exhibit a series of new examples of rigid plane curves, that is, curves, whose collection of singularities determines them almost uniquely up to a projective transformation of the plane.
A new family of maximal curves over a finite field is presented and some of their properties are investigated.
We consider mixed types of not only regular curves but also curves with singular points in the Lorentz-Minkowski 3-space. In order to consider mixed type of curves with singular points, we consider the lightcone frame and lightcone framed…
In this paper we begin to study curves on a weighted projective plane with one trivial weight, ${\mathbb P}(1,m,n)$, by determining the genus of curves of Fermat type. These are curves defined by a ``homogeneous'' polynomial analagous to…
In this paper, we define some new associated curves as integral curves of a vector field generated by Frenet vectors of tangent indicatrix of a curve in Euclidean 3-space. We give some relationships between curvatures of these curves. By…
In this paper, we investigate constant breadth curves on a surface according to Darboux frame and give some characterizations of these curves.
In this study, we investigate Bertrand curves in three dimensional dual space D3 and we obtain the characterizations of these curves in dual space D3. Also we show that involutes of a curve constitute Bertrand pair curves.
We take the fundamental group of the complement of the branch curve of a generic projection induced from canonical embedding of a surface. This group is stable on connected components of moduli spaces of surfaces. Since for many classes of…
We define the type of a plane curve as the initial degree of the corresponding Bourbaki ideal. Then we show that this invariant behaves well with respect to the union of curves. Curves of type $0$ are precisely the free curves, while curves…
We introduce a new class of surfaces in Euclidean $3$-space, called surfaces of osculating circles, using the concept of osculating circle of a regular curve. These surfaces contain a uniparametric family of planar lines of curvature. In…
In this study, the new characterizations of special curves are investigated without using the curvatures of these special curves: general helices, slant helices, Bertrand curves, Mannheim curves. The curvatures are given by the help of the…
We bound the genus of a projective curve lying on a complete intersection surface in terms of its degree and the degrees of the defining equations of the surface on which it lies.