  Here, an analytical version of numerical results is obtained in case of
considering the laminar non-turbulent limit, of a twisted Riemannian thin flux
tube. It is shown that the magnetic field is amplified, when electric current
helicity and Riemann curvature are both negative. Thus spaces of positive and
negative Riemannian curvatures seems to support dynamo action inside the torus,
and not only negative Riemannian curvature surfaces as happens in 2D dynamos.
New features appear in ${\alpha}^{2}$-dynamo twisted flow, using the
approximation of thin tubes flux tubes. These solutions are obtained in the
resonant profile of the toroidal and poloidal frequencies modes of the dynamo
force-free flow.
