A new approach for magnetic curves in 3D Riemannian manifolds

2014/05/01 by Zehra Bozkurt, Ismail Gök, Yusuf Yaylı +1 · 5 citations
Mathematics · #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems #Nonlinear Partial Differential Equations

paper · doi:10.1063/1.4870583

Abstract

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 paper, we give a new variational approach to study the magnetic flow associated with the Killing magnetic field in a three-dimensional oriented Riemann manifold, (M3, g). And then, we investigate the trajectories of the magnetic fields called as N-magnetic and B-magnetic curves.

Citations

• Magnetic curves corresponding to Killing magnetic fields in \mathbb E³E3
• Magnetic vortex filament flows
• General helices and a theorem of Lancret

Cited by

• A non-Newtonian magnetic curves in multiplicative Riemann manifolds
• Dual magnetic curves and flux ruled surfaces
• Magnetic flux surfaces and magnetic curves with Bishop frame in Euclidean 3-space
• Geometric properties of lightlike magnetic curves and magnetic flux surfaces in Minkowski 3-space
• Optical hausdorff quantum energy of spherical magnetic particles. [europepmc]

Related

• Magnetic curves corresponding to Killing magnetic fields in \mathbb E³E3
• Magnetic flows on 3D contact sub-Riemannian manifolds via the Rumin complex
• Flux ruled surfaces and the magnetic curves obtained from the curvature theory
• A non-Newtonian magnetic curves in multiplicative Riemann manifolds
• Magnetic flux surfaces and magnetic curves with Bishop frame in Euclidean 3-space