Abstract
It is shown that the foliation of a space-time manifold of codimension 2 provides a basis for the study of the deformation of magnetic field lines. It is found that the fluid flow vector and the curvature vector of a nongeodesic “stiff” magnetic field line are always orthogonal. Further, it is shown that the metric tensor of the 2-space orthogonal to the “Maxwellian string” is Lie-transported along the magnetic field lines when the magnetic field lines are “stiff.” If there exists a spacelike Killing vector field parallel to the magnetic field, then the magnetic field lines must be “stiff.”
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