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- W4301243013 abstract "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." @default.
- W4301243013 created "2022-10-05" @default.
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- W4301243013 date "2010-11-11" @default.
- W4301243013 modified "2023-09-27" @default.
- W4301243013 title "Smooth metric measure spaces and quasi-Einstein metrics" @default.
- W4301243013 doi "https://doi.org/10.48550/arxiv.1011.2723" @default.
- W4301243013 hasPublicationYear "2010" @default.
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