  The anomalous Hall effect is investigated theoretically by means of density
functional calculations for the non-collinear antiferromagnetic order of the
hexagonal compounds Mn$_3$Ge and Mn$_3$Sn using various planar triangular
magnetic configurations as well as unexpected non-planar configurations. The
former give rise to anomalous Hall conductivities (AHC) that are found to be
extremely anisotropic. For the planar cases the AHC is connected with
Weyl-points in the energy-band structure, which are described in detail. If
this case were observable in Mn$_3$Ge, a large AHC of about 900 S/cm should be
expected. However, in Mn$_3$Ge it is the non-planar configuration that is
energetically favored, in which case it gives rise to an AHC of 100 S/cm. The
non-planar configuration allows a quantitative evaluation of the topological
Hall effect that is seen to determine this value of the conductivity to a large
extent. For Mn$_3$Sn it is the planar configurations that are predicted to be
observable. In this case the AHC can be as large as 250 S/cm.
