  Smooth metric measure spaces have been studied from the two different
perspectives of Bakry-\'Emery and Chang-Gursky-Yang, both of which are closely
related to work of Perelman on the Ricci flow. These perspectives include a
generalization of the Ricci curvature and the associated quasi-Einstein
metrics, which include Einstein metrics, conformally Einstein metrics, gradient
Ricci solitons, and static metrics. In this article, we describe a natural
perspective on smooth metric measure spaces from the point of view of conformal
geometry and show how it unites these earlier perspectives within a unified
framework. We offer many results and interpretations which illustrate the
unifying nature of this perspective, including a natural variational
characterization of quasi-Einstein metrics as well as some interesting families
of examples of such metrics.
