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Quasi-Einstein Metrics and Conformal Geometry

QMAP Seminar

Speaker: Jeffrey Case, UCSB
Location: 2112 MSB
Start time: Wed, May 18 2011, 3:10PM

Quasi-Einstein Metrics are an important class of metrics which include Einstein metrics, static metrics, and gradient Ricci solitons. Except for gradient Ricci solitons, these metrics all admit a natural formulation in conformal geometry. Nevertheless, this formulation still yields insights into gradient Ricci solitons. We will introduce this conformally invariant formulation, and illustrate its utility in two contexts. First, we will use it to prove a precompactness theorem for compact quasi-Einstein metrics, yielding in particular convergence to gradient Ricci solitons. Second, we will use it to introduce the tractor calculus to quasi-Einstein metrics, which will yield some insights into the basic structure of quasi-Einstein metrics.