Notes on magnetic curves in 3D semi-Riemannian manifolds

Ozdemir Z., GÖK İ., YAYLI Y., EKMEKCİ F. N.

TURKISH JOURNAL OF MATHEMATICS, cilt.39, sa.3, ss.412-426, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 39 Sayı: 3
  • Basım Tarihi: 2015
  • Doi Numarası: 10.3906/mat-1408-31
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.412-426
  • Anahtar Kelimeler: Special curves, vector fields, flows, ordinary differential equations, HELICES
  • Ankara Üniversitesi Adresli: Evet

Özet

A magnetic field is defined by the property that its divergence is zero in three-dimensional semi-Riemannian manifolds. Each magnetic field generates a magnetic flow whose trajectories are curves gamma, called magnetic curves. In this paper, we investigate the effect of magnetic fields on the moving particle trajectories by variational approach to the magnetic flow associated with the Killing magnetic field on three-dimensional semi-Riemannian manifolds. We then investigate the trajectories of these magnetic fields and give some characterizations and examples of these curves.