Title:  Warped product Einstein structure

Abstract: The construction of Einstein metrics on warped products has been widely used in general relativity, including the Schwarzschild metric. The study of such construction on Riemannian manifolds already appeared in Besse's book on Einstein manifolds. A new perspective of study was introduced by Case-Shu-Wei in 2008. They studied the Einstein metrics on warped products through the equation for the Ricci curvature of the base manifold. In this talk, I will present a few recent results on warped product Einstein metrics: the classification with interesting geometries, the uniqueness of such metrics, and the connection with non-gradient expanding Ricci solitons. It is based on the joint work with Peter Petersen (UCLA) - William Wylie (Syracuse), and with Qiang Chen.