Related papers: Magnetic Curves in $C$-manifolds

For almost contact metric or almost paracontact metric manifolds there is natural notion of $\eta$-normality. Manifold is called $\eta$-normal if is normal along kernel distribution of characteristic form. In the paper it is proved that…

In this article we investigate regular curves whose derivatives have vanishing mean oscillations. We show that smoothing these curves using a standard mollifier one gets regular curves again. We apply this result to solve a couple of open…

Contact path geometries are curved geometric structures on a contact manifold comprising smooth families of paths modeled on the family of all isotropic lines in the projectivization of a symplectic vector space. Locally such a structure is…

Experimentally observed magnetic fields with nanoscale variations are theoretically modeled by a piece-wise constant function with jump discontinuity along a smooth curve, the magnetic edge. Assuming the edge is a closed curve with an axis…

Examples are presented of how the geometric notion of the mean curvature is used for general magnetic field configurations and magnetic surfaces. It is shown that the mean magnetic curvature is related to the variation of the absolute value…

We prove that closed manifolds admitting a generic metric whose sectional curvature is locally quasi-constant are graphs of space forms. In the more general setting of QC spaces where sets of isotropic points are arbitrary, under suitable…

Complex contact manifolds have recently received considerable attention. Many of the newer publications approach contact manifolds via the covering family of minimal rational curves. This short note furthers the study of these curves. It is…

This note is about uniform, plane, singly connected, regular Hall-plates with an arbitrary number of contacts exposed to a uniform magnetic field of arbitrary strength. In practice, the regular symmetry is the most common one. If the…

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…

This work presents the magnetic field geometry in a complex of three cometary (with head-tail morphology) globules, namely LDN 323, LDN 328, and LDN 331, using R-band polarization measurements of background stars. These observations were…

Magnetic clouds (MCs) are "magnetized plasma clouds" moving in the solar wind. MCs transport magnetic flux and helicity away from the Sun. These structures are not stationary but feature temporal evolution. Commonly, simplified MC models…

Magnetic, chemically peculiar stars are known for exhibiting surface abundance inhomogeneities (chemical spots) that lead to photometric and spectroscopic variability with the rotation period. It is commonly assumed that the surface…

We determine the curvature equations of natural metrics on tangent bundles and radius r tangent sphere bundles S_rM of a Riemannian manifold M. A family of positive scalar curvature metrics on S_rM is found, for any M with bounded sectional…

In this paper we give some positive and negative results about the contact property for the energy levels $\Sigma_c$ of a symplectic magnetic field on $S^2$. In the first part we focus on the case of the area form on a surface of…

Legendre curves play a very important and special role in geometry and topology of almost contact manifolds.There are certain results known for Legendre curves in 3-dimensional normal almost contact manifolds. The aim of this paper is to…

The optical conductivity of graphene, bilayer graphene, and graphite in quantizing magnetic fields is studied. Both dynamical conductivities, longitudinal and Hall's, are analytically evaluated. The conductivity peaks are explained in terms…

In this paper we prove the path connectedness of the moduli spaces of metrics with positive isotropic curvature on certain compact four-dimensional manifolds.

This paper develops new links between contact geometry, magnetic dynamics, and symmetry in exact magnetic systems. First, we establish an interpolation property for Killing magnetic systems on contact manifolds under an additional…

We develop an approach to treat magnetic energy of a ferromagnet for arbitrary curved wires and shells on the assumption that the anisotropy contribution much exceeds the dipolar and other weak interactions. We show that the curvature…

We find that in the kinematic limit the ensemble averaged square of the curvature of magnetic field lines is exponentially amplified in time by the turbulent motions in a highly conductive plasma. At the same time, the ensemble averaged…