Related papers: Osculating direction curves and their applications
We classify the self-similar solutions to a class of Weingarten curvature flow of connected compact convex hypersurfaces, isometrically immersed into space forms with non-positive curvature, and obtain a new characterization of a sphere in…
In this paper, we de\"One a new type curve as V-Mannheim curve, V Mannheim partner curve and generating curve of Mannheim curve. We give characterization of these curve. In addition, we study a relation between Mannheim curve and spherical…
In this study, we give the relation of being general helix and slant helix of two curves by using the equation between them. Also we find some results and express the characterizations of these curves.
Some new kinds of special curves called $\overset{\_}{\xi}$-helix, $\overset{% \_}{\xi}_{1}$-helix, $\overset{\_}{\mu}$-helix, $\overset{\_}{\nu}$-helix and $W_{k}$-Darboux helices $(k\in \left\{ {n,r,o}\right\} )$ in the Myller…
In this paper, the general formulation for inextensible flows of curves on oriented surface in $\mathbb{R}^3 $ is investigated. The necessary and sufficient conditions for inextensible curve flow lying an oriented surface are expressed as a…
This article defines a new family of curves in space, whose graphs generate shapes similar to whirls. An intrinsic equation is found, in terms of curvature and torsion, which gives necessary and sufficient conditions for the existence of…
In this study, some new types of timelike general helices associated to a non-lightlike curve are introduced in Minkowski 3-space. These new helices are called associated timelike helices. Some special types of associated timelike helices…
Here we explore the geometry of the osculating spaces to projective varieties of arbitrary dimension. In particular, we classify varieties having very degenerate higher order osculating spaces and we determine mild conditions for the…
We consider ruled surfaces in the three-dimensional Euclidean space and some geometrically distinguished families of curves on them whose normal curvature has a concrete form. The aim of this paper is to find and classify all ruled surfaces…
A space curve in a Euclidean 3-space $\mathbb E^3$ is called a rectifying curve if its position vector field always lies in its rectifying plane. This notion of rectifying curves was introduced by the author in [Amer. Math. Monthly {\bf…
In this paper, we focus on some characterizations for curves in the Galilean and Pseudo-Galilean space.
The paper is devoted to differential geometric invariants determining a Frenet curve in up to a direct similarity These invariants can be presented by the Euclidean curvatures in terms of an arc lengths of the spherical indicatrices. Then,…
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…
We extend the old definition of the Apollonius circle in such a way that it results in the same curve in Euclidean geometry but will be more convenient in hyperbolic and spherical geometries. We show that there exists an Apollonius circle…
In this paper, we introduce isophote curves on surfaces in Galilean 3-space. Apart from the general concept of isophotes, we split our studies into two cases to get the axis d of isophote curves lying on a surface such that d is an…
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…
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…
In this study, we consider AW(k)-type curves according to the Bishop Frame in Euclidean space E^3. We give the relations between the Bishop curvatures k_1, k_2 of a curve in E^3.
In this paper, we revisit the classical problem of determining osculating conics and sextactic points for a given algebraic curve. Our focus is on a particular family of plane cubic curves known as the Hesse pencil. By employing classical…
The present paper deals with some characterizations of rectifying and osculating curves on a smooth surface with respect to the reference frame $\{\vec{T},\ \vec{N},\ \vec{T}\times\vec{N}\}$. We have computed the components of position…