Mariño-Villar, Rodrigo2023-03-142023-03-142023Journal of Geometry and Physics 186 (2023) 1047540393-0440http://hdl.handle.net/10347/30308It is given a complete study of locally conformally flat metrics satisfying some weakly-Einstein conditions. It is shown that they are either a product Mn(c)xMn(-c) or a warped product RxfRn-1 for some specific warping function. Moreover, some conditions on locally conformally flat fixed points for the RG2 flow are pointed outeng©2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/)http://creativecommons.org/licenses/by/4.0/Critical metricEinstein and weakly-Einstein metricsLocally conformally flatTwo-loop renormalization flowjournal article10.1016/j.geomphys.2023.104754open access