Inserted: 7 oct 2010
Last Updated: 3 jun 2013
Journal: J. Reine Angew. Math. (Crelle's Journal)
Volume: 675 (2013)
In this paper we prove that any complete locally conformally flat quasi-Einstein manifold of dimension $n\geq 3$ is locally a warped product with $(n-1)$-dimensional fibers of constant curvature. This result includes also the case of locally conformally flat gradient Ricci solitons.