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The topological mapping between a torus of big radius and a sphere is appliedto the Riemannian geometry of a stretched and twisted very thick magnetic fluxtube, to obtain spherical dynamos solving the magnetohydrodynamics (MHD)self-induction equation for the magnetic flux tubes undergoing differential(non-uniform) rotation along the tube magnetic axis. Constraints on the shearis also computed. It is shown that when the hypothesis of the convectivecyclonic dynamo is used the rotation is constant and a solid rotational body isobtained. As usual toroidal fields are obtained from poloidal magnetic fieldand these fields may be expressed in terms of the differential rotation${\Omega}(r,{\theta}(s))$. In the case of non-cyclonic dynamos the torsion inthe Frenet frame is compute in terms of the dynamo constant. The flux tubeshear $\frac{\partial}{{\partial}r}{\Omega}$ is also computed. The untwistedtube case is shown to be trivial in the sense that does not support any dynamoaction. This case is in agreement with Cowling antidynamo theorem, since in theuntwisted case the tube becomes axially symmetric which the refereed theoremrules out. We also show that it is consistent with the Zeldovich antidynamotheorem which rules out planar dynamos. Knowledge of the differential rotationof the Earth, for example, allows one to place limits on the curvature andtorsion of the flux tube axis and vice-versa, knowledge of the topology permitus to infer differential rotation and other physical parameters of the starsand planets.

Differential rotation of stretched and twisted thick magnetic flux tube dynamos in Riemannian spaces