  Two examples of magnetic anti-dynamos in magnetohydrodynamics (MHD) are
given. The first is a 3D metric conformally related to Arnold cat fast dynamo
metric: ${ds_{A}}^{2}=e^{-{\lambda}z}dp^{2}+e^{{\lambda}z}dq^{2}+dz^{2}$ is
shown to present a behaviour of non-dynamos where the magnetic field
exponentially decay in time. The curvature decay as z-coordinates increases
without bounds. Some of the Riemann curvature components such as $R_{pzpz}$
also undergoes dissipation while component $R_{qzqz}$ increases without bounds.
The remaining curvature component $R_{pqpq}$ is constant on the torus surface.
The other anti-dynamo which may be useful in plasma astrophysics is the thin
magnetic flux rope or twisted magnetic thin flux tube which also behaves as
anti-dynamo since it also decays with time. This model is based on the
Riemannian metric of the magnetic twisted flux tube where the axis possesses
Frenet curvature and torsion. Since in this last example the Frenet torsion of
the axis of the rope is almost zero, or the possible dynamo is almost planar it
satisfies Zeldovich theorem which states that planar dynamos do not exist.
Changing in topology of this result may result on a real dynamo as discussed.
