{"paper":{"title":"Compact almost Ricci solitons with constant scalar curvature are gradient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Abd\\^enago Barros, Ernani Ribeiro Jr, Rondinelle Batista","submitted_at":"2012-09-12T20:22:55Z","abstract_excerpt":"The aim of this note is to prove that any compact non-trivial almost Ricci soliton $\\big(M^n,\\,g,\\,X,\\,\\lambda\\big)$ with constant scalar curvature is isometric to a Euclidean sphere $\\Bbb{S}^{n}$. As a consequence we obtain that every compact non-trivial almost Ricci soliton with constant scalar curvature is gradient. Moreover, the vector field $X$ decomposes as the sum of a Killing vector field $Y$ and the gradient of a suitable function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2720","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"}