2/5/2010

Will Wylie
University of Pennsylvania

On m-Quasi Einstein metrics

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.