On mQuasi Einstein metrics
On mQuasi Einstein metrics

Will Wylie, University of Pennsylvania
Fine Hall 314
We say an $n$dimensional Riemannian manifold is an $m$Quasi Einstein metric if it is the base of an $(n+m)$dimensional warped product Einstein manifold. We view the $m$Quasi Einstein equation as a generalization of the Einstein equation (since an Einstein manifold is the base of a trivial product Einstein manifold). The $m$Quasi Einstein equation is also closely related to the gradient Ricci soliton equation. In this talk I will give an overview of some earlier results about the classification of $m$quasi Einstein metrics and prove a new classification of $m$Quasi Einstein metrics with harmonic curvature. This is joint work with Peter Petersen and Chenxu He.