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 of the sources. Our study investigates systematically, for the first time, the relationship between the two energy regimes in radio galaxies. In this first paper, we focus on Fermi-LAT-detected sources. The TANAMI program monitors a large sample of radio-loud AGN at 8.4GHz and 22.3GHz with the Australian Long Baseline Array(LBA) and associated telescopes in Antarctica, Chile, New Zealand and South Africa. 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 such as speed and viewing angle. We analyzed103 months of 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, which appears to be a defining feature of high-energy emitting Fanaroff-Riley type II radio galaxies. 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, which is not accompanied by variations in the VLBI jet. We robustly confirm the presence of significant superluminal motion, up to {beta}app~3, in the jet of the TeV radio galaxy PKS 0625-35. Our VLBI results constrain the jet viewing angle to be {theta}<53{deg}, allowing for the possibility of a closely aligned jet. Finally, by analyzing the first pc-scale multi-epoch images of the prototypical Compact Symmetric Object (CSO) PKS 1718-649, we place an upper limit on the separation speed between the two mini-lobes, which in turn allows us to derive a lower limit on the age of the source.Conclusions.We can draw some preliminary conclusions on the relationship between pc-scale jets and gamma-ray emission in radio galaxies, basedonFermi-LAT-detected sources with available multi-epoch VLBI measurements. 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 common indicators of jet Doppler boosting. This seems to indicate that gamma-ray emission in radio galaxies is not driven by orientation-dependent effects, as in blazars, which is consistent with the unified model of jetted AGN.

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