{"paper":{"title":"The Prescribed Ricci Curvature Problem on Three-Dimensional Unimodular Lie Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Timothy Buttsworth","submitted_at":"2016-07-12T05:34:24Z","abstract_excerpt":"Let G be a three-dimensional unimodular Lie group, and let T be a left-invariant symmetric (0, 2)-tensor field on G. We provide the necessary and sufficient conditions on T for the existence of a pair (g, c) consisting of a left-invariant Riemannian metric g and a positive constant c such that Ric(g) = cT, where Ric(g) is the Ricci curvature of g. We also discuss the uniqueness of such pairs and show that, in almost all cases, there exists at most one positive constant c such that Ric(g) = cT is solvable for some left-invariant Riemannian metric g."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03233","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"}