Averaged description of the magnetic field in the hydro-magnetic dynamo problem

Various magnetic mean-field dynamo problems are discussed. We demonstrate the differences from the classic case and the additional restrictions for the correlation tensor in the case of non-Euclidean space, as well as in the case of complex topology. We have shown a much more rapid growth of the magnetic energy density in the Lobachevsky space. We found that the standard methods of deriving the mean-field equation are ineffective in the case of $\alpha$-fluctuations.