2008/03/05 by L Garcia de Andrade, de Andrade, L Garcia
Biochemistry, Genetics and Molecular Biology · Earth and Planetary Sciences · Physics and Astronomy · #14J32 #FOS: Physical sciences #Geomagnetism and Paleomagnetism Studies #Geophysics and Gravity Measurements #Mathematical Physics (math-ph) #Solar and Space Plasma Dynamics
paper · pdf · doi:10.48550/arxiv.0803.0637
openalex publication_date 2008/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.