  It is shown that C-flows in Riemannian three-dimensional compact manifold can
be naturally considered as generalized dynamo Arnold's metric in compact
manifolds, the so-called cat map dynamo. The generalized solution of
self-induction equation in the background of this metric shows that one is
allowed to consider stretching along both directions of the flow, instead of
compressed in one direction and stretched in the other such as in Arnold's
dynamo. Though this solution can be considered as unrealistic,at least for
incompressible flows, there is another generalized solution which considers
distinct stretch and compression intensities along distinct directions.
Curvature tensor components are computed by making use of calculus of
differential forms.
