| Résume | In this talk, we will show some results about quasi-Einstein manifolds.Quasi-Einstein manifolds can be characterized as bases of Einstein warped products. In the first part, we investigated the infinity structure of a complete non- compact quasi-Einstein manifold. In particular, we show that if M is a base of a Ricci-flat 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 non-parabolic and, on agiven hypothesis about scalar curvature, M has only one end f-non-parabolic. In addition, we obtain two estimates for the volume of the geodesic balls of M. In the second part, we will show that Bach-flat non-compact quasi-Einstein 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.
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