The concept of statistical homogeneity and isotropy for vector fields for cosmological models with multiply connected space sections is analyzed. Considering a flat 3D torus as an example, it is shown that the correlation tensor of a statistically homogeneous and isotropic (locally) solenoidal vector field in this case depends on a countable set of functions corresponding to various classes of geodesics connecting the points in which the tensor is calculated. In contrast, such a tensor in a simply connected Universe depends on just one function.
$^1$Department of Probability Theory, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia
$^2$Department of Mathematics, Faculty of Physics, Moscow State University, Moscow, 119991, Russia
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