Résume  In this talk, we will show some results about quasiEinstein manifolds.QuasiEinstein manifolds can be characterized as bases of Einstein warped products. In the first part, we investigated the infinity structure of a complete non compact quasiEinstein manifold. In particular, we show that if M is a base of a Ricciflat warped product then M is connected at infinity. When M is the basis of an Einstein warped product with Einstein constant λ <0, there are examples with more than one end. In this case, we show that M is nonparabolic and, on agiven hypothesis about scalar curvature, M has only one end fnonparabolic. In addition, we obtain two estimates for the volume of the geodesic balls of M. In the second part, we will show that Bachflat noncompact quasiEinstein manifolds with λ = 0 and positive Ricci curvature are isometric to a rotationally symmetric metric whose fiber is a Einstein manifold.
This is a joint work with R. Batista and E. Ribeiro Jr.
