  Recently Guenther et al the globally diagonalized ${\alpha}^{2}$ dynamo
operator spectrum [J Phys A 2007) in mean field media, and its Krein space
related perturbation theory [J Phys A 2006). Earlier, an example of fast
dynamos in stretch shear and fold Anosov maps have been given by Gilbert [PRSA
[1993)). In this paper, analytical solutions representing general turbulent
dynamo filaments are obtained in resistive plasmas. When turbulent diffusivity
is present and kinetic helicity vanishes, a fast dynamo mode is obtained, and
the Anosov eigenvalue obtained. The magnetic field lays down on a Frenet 2
plane along the filaments embedded in a 3D flow. Curvature effects on fast
dynamo are also investigate. In case of weak curvature filaments the one
dimensional manifolds in plasmas present a fast dynamo action. A parallel
result has been obtained by Chicone et al [Comm Math Phys), in the case fast
dynamo spectrum in two dimensional compact Riemannian manifolds of negative
constant curvature, called Anosov spaces. While problems of embedding may
appear in their case here no embedding problems appear since the one
dimensional curved plasmas are embedded in three dimensional Euclidean spaces.
In the examples considered here, equipartion between normal and binormal
components of the magnetic field components is considered. In the opposite
case, non Anosov oscillatory, purely imaginary, branches of the spectrum are
found in dynamo manifold. Negative constant curvature non-compact
$\textbf{H}^{2}$ manifold, has also been used in one-component electron 2D
plasma by Fantoni and Tellez (Stat. Phys, (2008))
