Locally conformally flat weakly-Einstein manifolds

It is shown that locally conformally flat weakly-Einstein manifolds are either locally symmetric, and hence a product $$N_1^m(c)\times N_2^m(-c)$$ , or otherwise they are locally homothetic to some specific warped product metrics $${\mathcal {I}}\times _fN(c)$$ . As an application we classify weakly-Einstein hypersurfaces in the Euclidean space.