Related papers: On Spherical Slant Helices in Euclidean 3-Space
In this study, we have identified $V_3$ slant helix ($2^{nd}$ type slant helix, $V_5$ slant helix ($3^{rd}$ type slant helix) and attained some characteristic properties in the Euclidean 5-Space $E^5$. In addition to this, we have proven…
In this work, notion of a slant helix is extended to space E$^n$. Necessary and sufficient conditions to be a slant helix in the Euclidean $n-$space are presented. Moreover, we express some integral characterizations of such curves in terms…
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, in Euclidean n -space, we investigate the relation between slant helices and spherical helices. Moreover, in E n, we show that a slant helix and the tangent indicatrix of the slant helix have the same axis (or direction).…
In this work, we give some new characterizations for inclined curves and slant helices in n-dimensional Euclidean space E^{n}. Morever, we consider the pre-characterizations about inclined curves and slant helices and reconfigure them.
In this paper, we investigate spacelike slant helix in $H_{0}^{2}$ and $S_{1}^{2}$ and we obtain parametric equation of spherical slant helix in $H_{0}^{2}$ and $S_{1}^{2}$. Also related examples and their illustrations are given.
In this paper we characterize concircular helices in $R^3$ by means of a differential equation involving their curvature and torsion. We find a full description of concircular surfaces in $R^3$ as a special family of ruled surfaces, and we…
In this paper, we define a new special curve in Euclidean 3-space which we call {\it $k-$slant helix} and introduce some characterizations for this curve. This notation is generalization of a general helix and slant helix. Furthermore, we…
In this paper, we give smoe characterizations of relatively normal-slant helices and isophotic curves on a smooth surface immersed in Euclidean 3-space with respect to their position vevtor. We also introduce the methods for generating an…
In this paper, we study helices and the Bertrand curves. We obtain some of the classification results of these curves with respect to the modified orthogonal frame in Euclidean 3-spaces.
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 work, we studied the properties of the spherical indicatrices of involute curve of a space curve and presented some characteristic properties in the cases that involute curve and evolute curve are slant helices and helices,…
In this paper, we investigate timelike slant helix in $S_{1}^{2}$ and we obtain parametric equation of timelike slant helix in $S_{1}^{2}$. Also related examples and their illustrations are given.
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…
A new kind of partner curve called osculating mate of a Frenet curve is introduced. Some characterizations for osculating mate are obtained and using the obtained results some special curves such as slant helix, spherical helix, $C$-slant…
By considering a spatial curve in a Euclidean space, we use its components, together with attaining a cyclic matrix, to show that this matrix is homothetic too and is in correspondence with a homothetic motion. Furthermore, if the curve…
In this study, we define some new types of ruled surfaces called slant ruled surfaces. We give some characterizations for a regular ruled surface to be a slant ruled surface in Euclidean 3- space. We show that if the slant ruled surface is…
We consider a curve $\alpha=\alpha(s)$ in Minkowski 3-space $E_1^3$ and denote by $\{T,N,B}$ the Frenet frame of $\alpha$. We say that $\alpha$ is a slant helix if there exists a fixed direction $U$ of $E_1^3$ such that the function…
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…
We introduce semi-helix hyper surfaces of Euclidean spaces. We also provide a local characterization of how these semi-helices are constructed.