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A new antidynamo theorem for non-stretched twisted magnetic flux tube dynamois obtained. Though Riemannian curvature cannot be neglected since oneconsiders curved magnetic flux tube axis, the stretch can be neglect since oneonly considers the limit of thin magnetic flux tubes. The theorem states thatmarginal or slow dynamos along curved (folded), torsioned (twisted) andnon-stretched flux tubes endowed with diffusionless plasma flows, if aconstraint is imposed on the relation between poloidal and toroidal magneticfields in the helical dynamo case. A formula for the stretch of flux tubes isderived. From this formula one shows that the Riemann flux tube is stretched byan interaction between the plasma flow vorticity and torsion, in accordancewith our physical intuition. Marginal diffusionless dynamos are shown to existobtained in the case of flux tube dynamos exponential stretching. Thus slowdynamos can be obtaining on the flux tube under stretching. Filamentary dynamosanti-dynamos are also considered. As flux tubes possess a magnetic axistorsioned filament, it can also be considered as thegerm of a fast dynamo influx tubes Riemannian curved space. It is shown that for non-stretchedfilaments only untwist and unfold filaments can provide dynamo action indiffusive case. A condition for exponential stretching and fast dynamos infilaments is given. These results are actually in agreement with Vishikargument that fast dynamo cannot be obtained in non-stretched flows. Actuallythe flux tube result is the converse of Vishik's lemma.

Exponential stretching in filaments as fast dynamos in Euclidean and Riemannian 3D spaces