Related papers: On Spherical Slant Helices in Euclidean 3-Space
In this article we study polyharmonic curves of constant curvature where we mostly focus on the case of curves on the sphere. We classify polyharmonic curves of constant curvature in three-dimensional space forms and derive an explicit…
We explore geometric properties of circular analogues of tractrices and pseudospheres in $\mathbb R^3$.
We define a new kind of helicoidal surface of value m. A rotational surface which is isometric to the helicoidal surface of value m is revealed. In addition, we calculate some differential geometric properties of the helicoidal surface of…
The article reviews some of the (fairly scattered) information available in the mathematical literature on the subject of angles in complex vector spaces. The following angles and their relations are considered: Euclidean, complex, and…
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…
We introduce a local coordinate description for the correspondence between the space of oriented affine lines in Euclidean ${\Bbb{R}}^3$ and the tangent bundle to the 2-sphere. These can be utilised to give canonical coordinates on surfaces…
This paper is a continuation of the papers [2,3,4,5,6]. In this paper the osculating spaces of arbitrary order of a manifold embedded in Euclidean space are considered. A better estimation of their dimensions as well as the description of…
In this study, we give the relationships between the conical curvatures of ruled surfaces drawn by the unit vectors of the ruling, central normal and central tangent of a regular ruled surface in the Euclidean -space. We obtain the…
We study those Lagrangian surfaces in complex Euclidean space which are foliated by circles or by straight lines. The former, which we call cyclic, come in three types, each one being described by means of, respectively, a planar curve, a…
Spherical localisation is a technique whose history goes back to M.Gromov and V.Milman. It's counterpart, the Euclidean localisation is extensively studied and has been put to great use in various branches of mathematics. The purpose of…
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…
We consider skew 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…
We investigate the relationship among characteristic curves on developable surfaces. In case parameter curves coincide with these curves, we show that the base curve of a developable surface could be either a plane curve, a circular helix,…
In this study, some characterizations of Euler spirals in E_1^{3} have been presented by using their main property that their curvatures are linear. Moreover, discussing some properties of Bertrand curves and helices, the relationship…
We establish some characterizations of elliptic hyperboloids (resp., ellipsoids) in the $(n+1)$-dimensional Euclidean space ${\Bbb E}^{n+1}$, using the $n$-dimensional area of the sections cut off by hyperplanes and the $(n+1)$-dimensional…
In this paper, we define a new kind of slant helix called f-eikonal V_{n}-slant helix in Pseudo- Riemannian manifolds and give the definition of harmonic curvature functions related to the f-eikonal V_{n}-slant helix in Pseudo- Riemannian…
We prove that a surface in Euclidean $3$-space has Maslovian normal bundle if and only if it is a part of a round sphere, a circular cylinder, or a circular cone.
We define two transforms between non-conformal harmonic maps from a surface into the 3-sphere. With these transforms one can construct, from one such harmonic map, a sequence of harmonic maps. We show that there is a correspondence between…
We consider a class of overdetermined problems in rotationally symmetric spaces, which reduce to the classical Serrin's overdetermined problem in the case of the Euclidean space. We prove some general integral identities for rotationally…
In this paper we describe the $\epsilon$-isothermic surfaces in the pseudo-Euclidean 3-space and we obtain the pseudo-Calapso equation. In sequence, we classify the Dupin surfaces in pseudo-Euclidean 3-space having distinct principal…