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

Abstract

It is given a complete study of locally conformally flat metrics satisfying some weaklyEinstein conditions. It is shown that they are either a product Mn(c)× Mn(−c) or a warped product R ×f Rn−1 for some specific warping function. Moreover, some conditions on locally conformally flat fixed points for the RG2 flow are pointed out.