  Earlier Arnold, Zeldovich, Ruzmaikin and Sokoloff [\textbf{JETP (1982)}] have
computed the eigenvalue of a uniform stretching torus transformation which
result on the first Riemann metric solution of the dynamo action problem.
Recently some other attempts to obtain Riemann metrics representing dynamo
action through conformal maps have been undertaken [{\textbf{Phys. Plasmas 14
(2007)}]. Earlier, Gilbert [\textbf{Proc. Roy. Soc. London A(2003)}] has
investigated a more realistic dynamo map solution than the one presented by
Arnold et al by producing a shearing of the Arnold's cat map, by eigenvalue
problem of a dynamo operator. In this paper, the eigenvalue of the Riemann
twisted torus dynamo flow metric is obtained as the ratio between the poloidal
and toroidal components of the flow. This result is obtained from the Euler
equation. In the twisted torus, the eigenvalue of the Riemann metric is
${m}_{\pm}=\frac{1\pm{\sqrt{5}}}{2}$, which is quite close to the value
obtained by Arnold. In the case the viscosity Reynolds number $Re\to{\infty}$,
the torus flow is unstable as one approaches the torus axis. In Arnold's dynamo
metric the eigenvalues are ${\chi}_{\pm}=\frac{3\pm{\sqrt{5}}}{2}$ which are
very close to the above value. Eigenvalues determine the growth rates of the
velocity ratio between poloidal and toroidal components of the flow. The curved
flow in torus follow previous work by Chen et al [\textbf{Phys Fluids (2006)}].
The ${\alpha}$-effect dynamo is shown to be a second-order effect in the torus
curvature and velocity flow. Loop dynamo flows and maps are also discussed.
