Structure of locally conformally flat manifolds satisfying some weakly-Einstein conditions

It 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) x Mn(-c) or a warped product R x f Rn-1 for some specific warping function. Moreover, some conditions on locally conformally flat fixed points for the RG2 flow are pointed out. (c) 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/).

Automated summary

A comprehensive study is conducted on locally conformally flat metrics satisfying weakly-Einstein conditions, which are shown to be either a product Mn(c) x Mn(-c) or a warped product R x f Rn-1 with a specific warping function. Additionally, some conditions on locally conformally flat fixed points for the RG2 flow are highlighted.