  Curvature and helicity topological bounds for the magnetic energy of the
streamlines magnetic structures of a kinematic dynamo flow are computed. The
existence of the filament dynamos are determined by solving the
magnetohydrodynamic equations for 3D flows and the solution is used to
determine these bounds. It is shown that in the limit of zero resistivity
filamentary dynamos always exists in the isotropic case, however when one takes
into account that the Frenet frame does not depend only of the filament length
parameter s, (anisotropic case) the existence of the filamentary dynamo
structure depends on the curvature in the case of screwed dynamos. Frenet
curvature is associated with forld and torsion to twist which allows us to have
a sretch, twist, and fold method to build fast filament dynamos. Arnold theorem
for the helicity bounds of energy of a divergence-free vector field is
satisfied for these streamlines and the constant which depends on the size of
the compact domain $M C R^{2}$, where the vector field is defined is determined
in terms of the dimensions of the constant cross-section filament. It is shown
that when the Arnold theorem is violated by the filament amplification of the
magnetic field structure appears, the magnetic field decays in space.
