  In the framework of the TANAMI multi-wavelength and VLBI monitoring, we study
the evolution of the parsec-scale radio emission in radio galaxies in the
southern hemisphere and their relationship to the $\gamma$-ray properties. In
this first paper, we focus on Fermi-LAT-detected sources. We perform a
kinematic analysis for five $\gamma$-ray detected radio galaxies using
multi-epoch 8.4 GHz VLBI images, deriving limits on intrinsic jet parameters.
We analyzed Fermi-LAT data in order to study possible connections between the
$\gamma$-ray properties and the pc-scale jets of Fermi-LAT-detected radio
galaxies, both in terms of variability and average properties. We discuss the
individual source results and draw preliminary conclusions on sample properties
including published VLBI results from the MOJAVE survey, with a total of
fifteen sources. We find that the first $\gamma$-ray detection of Pictor A
might be associated with the passage of a new VLBI component through the radio
core. For the peculiar AGN PKS 0521-36, we detect subluminal parsec-scale jet
motions, and we confirm the presence of fast $\gamma$-ray variability in the
source down to timescales of 6 hours. We robustly confirm the presence of
significant superluminal motion, up to $\beta_{app}\sim$3, in the jet of the
TeV radio galaxy PKS 0625-35. Finally, we place a lower limit on the age of the
Compact Symmetric Object (CSO) PKS 1718-649. We draw some preliminary
conclusions on the relationship between pc-scale jets and $\gamma$-ray emission
in radio galaxies. We find that the VLBI core flux density correlates with the
$\gamma$-ray flux, as seen in blazars. On the other hand, the $\gamma$-ray
luminosity does not show any dependence on the core brightness temperature and
core dominance, two indicators of Doppler boosting, suggesting that
$\gamma$-ray emission in radio galaxies is not driven by orientation-dependent
effects.
