  Examples of conformal dynamo maps have been presented earlier [Phys Plasmas
\textbf{14}(2007)] where fast dynamos in twisted magnetic flux tubes in
Riemannian manifolds were obtained. This paper shows that conformal maps, under
the Floquet condition, leads to coincidence between exponential stretching or
Lyapunov exponent, conformal factor of fast dynamos. Unfolding conformal dynamo
maps can be obtained in Riemann-flat manifolds since here, Riemann curvature
plays the role of folding. Previously, Oseledts [Geophys Astrophys Fluid Dyn
\textbf{73} (1993)] has shown that the number of twisted and untwisting orbits
in a two torus on a compact Riemannian manifold induces a growth of fast dynamo
action. In this paper, the stretching of conformal thin magnetic flux tubes is
constrained to vanish, in order to obtain the conformal factor for
non-stretching non-dynamos. Since thin flux tube can be considered as a twisted
or untwisting two-torus map, it is shown that the untwisting, weakly torsion,
and non-stretching conformal torus map cannot support a fast dynamo action, a
marginal dynamo being obtained. This is an example of an anti-fast dynamo
theorem besides the ones given by Vishik and Klapper and Young [Comm Math Phys
\textbf{173}(1996)] in ideally high conductive flow. From the Riemann curvature
tensor it is shown that new conformal non-dynamo, is actually singular as one
approaches the magnetic flux tube axis. Thus conformal map suppresses the
stretching directions and twist, leading to the absence of fast dynamo action
while Riemann-flat unfolding manifolds favors non-fast dynamos.
