{"paper":{"title":"Smooth metric measure spaces and quasi-Einstein metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jeffrey S. Case","submitted_at":"2010-11-11T18:04:06Z","abstract_excerpt":"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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2723","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}