Geodesic
Directional magnetic and electric vortex lines and their geometries in Minkowski space
Filomat, Tome 35 (2021) no. 3, p. 1015

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DOI

In this study, we firstly introduce a different type of directional Fermi-Walker transportations along with vortex lines of a non-vanishing vector field in three-dimensional Minkowski space. Then we consider some geometric quantities, which are used to characterize vortex lines, in order to express angular velocity vector (Darboux vector) of the system in terms of these quantities. Later we present timelike directional magnetic vortex lines by computing the Lorentz force. Hence, we reach a remarkable relation between timelike directional magnetic vortex lines and angular velocity vector of vortex lines with a non-rotating frame in Minkowski space. We also determine the timelike directional electric vortex lines by considering the electromagnetic force equation. We finally investigate the conditions of being uniform for magnetic fields of timelike directional magnetic vortex lines and we improve such a remarkable approach to find the electromagnetic curvature which contains many geometrical features belonging to timelike directional magnetic and electric vortex line
DOI : 10.2298/FIL2103015K
Classification : 53Z05, 81Q70
Keywords: Vortex lines, directional Fermi-Walker derivative, geometric phase, angular velocity vector, timelike directional magnetic and electric vortex lines, Minkowski space 
Talat Korpinar; Ridman Cem Demirkol. Directional magnetic and electric vortex lines and their geometries in Minkowski space. Filomat, Tome 35 (2021) no. 3, p. 1015 . doi: 10.2298/FIL2103015K
@article{10_2298_FIL2103015K,
     author = {Talat Korpinar and Ridman Cem Demirkol},
     title = {Directional magnetic and electric vortex lines and their geometries in {Minkowski} space},
     journal = {Filomat},
     pages = {1015 },
     year = {2021},
     volume = {35},
     number = {3},
     doi = {10.2298/FIL2103015K},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2103015K/}
}
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