|Responsables :||L. Hauswirth, R. Souam, E. Toubiana|
|Email des responsables :|
|Salle :||salle 2015|
|Adresse :||Sophie Germain|
Hébergé par le projet Géométrie et Dynamique de l’IMJ-PRG
|Orateur(s)||Marcos RANIERI - UFAL, Brésil,|
|Titre||On non-compact quasi-Einstein manifolds|
|Horaire||13:30 à 15:00|
|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.