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Frictional magnetic curves in 3D Riemannian manifolds

Talat Korpinar

Mathematics Department, Mus Alparslan University, Guzeltepe Campus, Mus 49100, Turkey

E-mail Address: talatkorpinar@gmail.com

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and

Ridvan Cem Demirkol

Mathematics Department, Mus Alparslan University, Guzeltepe Campus, Mus 49100, Turkey

E-mail Address: rcdemirkol@gmail.com

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https://doi.org/10.1142/S0219887818500202Cited by:71 (Source: Crossref)

Abstract

In this study, we investigate the special type of magnetic trajectories associated with a magnetic field $ℬ$ defined on a 3D Riemannian manifold. First, we consider a moving charged particle under the action of a frictional force, $f$ , in the magnetic field $ℬ$ . Then, we assume that trajectories of the particle associated with the magnetic field $ℬ$ correspond to frictional magnetic curves ( $f$ -magnetic curves $)$ of magnetic vector field $ℬ$ on the 3D Riemannian manifold. Thus, we are able to investigate some geometrical properties and physical consequences of the particle under the action of frictional force in the magnetic field $ℬ$ on the 3D Riemannian manifold.

Keywords:

AMSC: 78A35, 70K40, 53C15, 53C40, 53A17

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