Related papers: Magnetic Curves in $C$-manifolds

We consider slant normal magnetic curves in $(2n+1)$-dimensional $S$-manifolds. We prove that $\gamma $ is a slant normal magnetic curve in an $% S $-manifold $(M^{2m+s},\varphi ,\xi _{\alpha },\eta ^{\alpha },g)$ if and only if it belongs…

In $(2n+1)$-dimensional non-Sasakian contact metric manifolds, we consider Legendre curves whose mean curvature vector fields are $\mathcal{C}$-parallel or $\mathcal{C}$-proper in the tangent or normal bundles. We obtain the curvature…

Equations of the magnetization dynamics are derived for an arbitrary curved 2D surface. General static solutions are obtained in the limit of a strong anisotropy of both signs (easy-surface and easy-normal cases). It is shown that the…

A magnetic field is defined by the property that its divergence is zero in a three dimensional oriented Riemannian manifold. Each magnetic field generates a magnetic flow whose trajectories are curves called as magnetic curves. In this…

We study the motion of a charged particle under the action of a magnetic field with cylindrical symmetry. In particular we consider magnetic fields with constant direction and with magnitude depending on the distance $r$ from the symmetry…

In this paper, we study normal complex contact metric manifolds and we get some general results on them. Moreover, we obtained the general expression of the curvature tensor field for arbitrary vector fields. Furthermore, we show that the…

We define pseudo-Hermitian magnetic curves in Sasakian manifolds endowed with the Tanaka-Webster connection. After we give a complete classification theorem, we construct parametrizations of pseudo-Hermitian magnetic curves in…

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 investigate contact magnetic curves in the real special linear group of degree 2. They are geodesics of the Hopf tubes over the projection curve. We prove that periodic contact magnetic curves in SL(2,R) can be quantized in the set of…

Magnetic field lines in interstellar media have a rich morphology, which could be characterized by geometrical parameters such as curvature and torsion. In this paper, we explore the statistical properties of magnetic field line curvature…

In the present paper, we define and study $C$-parallel and $C$-proper slant curves of $S$-manifolds. We prove that a curve $\gamma $ in an $S$-manifold of order $r\geq 3,$ under certain conditions, is $C$-parallel or $C$-parallel in the…

In this paper, we firstly provide a concise overview of $\mathcal{S}-$manifolds, $f$-biharmonicity and $\theta _{\alpha }$-slant curves. We then derive a key equation and analyze it in detail to establish the necessary and sufficient…

In this work, we introduce the use of the differential geometry Frenet-Serret equations to describe a magnetic line in a pulsar magnetosphere. These equations, which need to be solved numerically, fix the magnetic line in terms of their…

We investigate the shapes of \gamma-ray pulsar light curves using 3D pulsar magnetosphere models of finite conductivity. These models, covering the entire spectrum of solutions between vacuum and force-free magnetospheres, for the first…

The interplay among the spectrum, geometry and magnetic field in tubular neighbourhoods of curves in Euclidean spaces is investigated in the limit when the cross section shrinks to a point. Proving a norm resolvent convergence, we derive…

Biharmonic or polyharmonic curves and surfaces in 3-dimensional contact manifolds are investigated.

The presented paper is devoted to study the curvature and torsion of slant Frenet curves in 3-dimensional normal almost paracontact metric manifolds. Moreover, in this class of manifolds, properties of non- Frenet slant curves (with null…

We present a concise definition of an electromagnetic curve on a Riemannian manifold and illustrate the explicit case of the motion of a charged particle on the unit sphere under the influence of a uniform magnetic field.

We consider the curvature radiation of the point-like charge moving relativistically along curved magnetic field lines through a pulsar magnetospheric electron-positron plasma. We demonstrate that the radiation power is largely suppressed…

Hamilton flows on K\"ahler manifold for which all trajectories are $H$-planar curves (complex analog of geodesics) are considered. These flows are called $H$-planar. The equation which has to obey the Hamiltonian of $H$-planar Hamilton flow…