Related papers: Magnetic curves corresponding to Killing magnetic …
The main aim of this paper is to study triharmonic curves in the 3-dimensional homogeneous space Sol. In the first part of the paper we shall obtain a complete classification of proper triharmonic curves with constant geodesic curvature and…
We determine all the possible torsion groups of elliptic curves over cyclic cubic fields, over non-cyclic totally real cubic fields and over complex cubic fields.
In this article we characterize all biharmonic curves of the Cartan-Vranceanu 3-dimensional spaces and we give their explicit parametrizations.
In this paper, we study the rectifying curves in multiplicative Euclidean space of dimension 3, i.e., those curves for which the position vector always lies in its rectifying plane. Since the definition of rectifying curve is affine and not…
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.
We give existence results for simple closed curves with prescribed geodesic curvature on $S^{2}$, which correspond to periodic orbits of a charge in a magnetic field.
We revise and generalize the properties of the electric and the magnetic scalar potentials in spacetimes admitting a Killing vector field: Their constancy on the Killing horizons, uniqueness of solution for the electromagnetic test fields…
A twisted curve in Euclidean 3-space E^3 can be considered as a curve whose position vector can be written as linear combination of its Frenet vectors. In the present study we study the twisted curves of constant ratio in E^3 and…
Defining the electric and magnetic field vectors in curved spacetime requires a proper choice of the observer's frame four-vector. Related literature shows that this fundamental issue in physics still needs to be properly resolved. In…
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.
For an elliptic curve $E$ defined over the field $\mathbb{C}$ of complex numbers, we classify all translates of elliptic curves in $E^3$ such that the $x$-coordinates satisfy a linear equation. This classification enables us to establish a…
The focus of this work is to analyze the trajectories of a point on the ellipsoid $\mathbb{S}_{a_{1},a_{2},a_{3}}^{2}$ while it is under the influence of a Killing vector field $K$. For this purpose, we introduce the generalized Darboux…
We investigate harmonic unit vector fields with totally geodesic integral curves on 3-manifolds. Under mild curvature assumptions, we classify both the vector fields and the manifolds that support them. Our results are inspired by…
We provide a description of W_3 transformations in terms of deformations of convex curves in two dimensional Euclidean space. This geometrical interpretation sheds some light on the nature of finite W_3-morphisms. We also comment on how…
We consider the evolution of electromagnetic fields in curved spacetimes and calculate the exact wave equations of the associated electric and magnetic components. Our analysis is fully covariant, applies to a general spacetime and isolates…
Exact solutions of the steady resistive three dimensional (3D) magnetohydrodynamics (MHD) equations in cylindrical coordinates for an incompressible plasma are presented. The solutions are translationally invariant along one direction and…
Killing vector fields in three dimensions play important role in the construction of the related spacetime geometry. In this work we show that when a three dimensional geometry admits a Killing vector field then the Ricci tensor of the…
We investigate modularity of elliptic curves over a general totally real number field, establishing a finiteness result for the set non-modular $j$-invariants. By analyzing quadratic points on some modular curves, we show that all elliptic…
As an introduction to the concept of "moduli space" we consider the moduli space of similarity classes of acute and right triangles in the plane. This has a map to the moduli space of elliptic curves which is onto and generically…
The well known formulas express the curvature and the torsion of a curve in $R^3$ in terms of euclidean invariants of its derivatives. We obtain expressions of this kind for all curvatures of curves in $R^n$. It follows that a curve in…