Locally conformally flat weakly-Einstein manifolds

摘要

It is shown that locally conformally flat weakly-Einstein manifolds are either locally symmetric, and hence a product N-1(m) (c) x N-2(m) (-c), or otherwise they are locally homothetic to some specific warped product metrics I x (f) N (c). As an application we classify weakly-Einstein hypersurfaces in the Euclidean space.