Rigidity of compact quasi-Einstein manifolds with boundary

Início: 05/04/2024 17:00

Término: 05/04/2024 18:00

Palestrante: Ernani Ribeiro Jr. (Universidade Federal do Ceará - UFC)

E-mail do Palestrante: ernani@mat.ufc.br

Resumo: In this talk, we discuss the geometry of compact quasi-Einstein manifolds with boundary. This topic is directly related to warped product Einstein metrics, static spaces and smooth metric measure spaces. We show that a 3-dimensional simply connected compact quasi-Einstein manifold with boundary and constant scalar curvature must be isometric to either the standard hemisphere $S^3_{+},$ or the cylinder $Itimes S^2$ with product metric. For dimension n=4, we prove that a 4-dimensional simply connected compact quasi-Einstein manifold with boundary and constant scalar curvature is isometric to either the standard hemisphere $S^4_{+},$ or the cylinder $Itimes S^3$ with product metric, or the product space $S^2_{+}times S^2$ with the doubly warped product metric. Other related results for arbitrary dimensions are also discussed. This is a joint work with J. Costa and D. Zhou.