{"paper":{"title":"Rigidity of complete non-compact generalized $m$-quasi-Einstein manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"M. Ahmad Mirshafeazadeh","submitted_at":"2026-06-04T13:16:13Z","abstract_excerpt":"We study complete non-compact gradient generalized m-quasi-Einstein manifolds with constant scalar curvature $R \\le 0$, soliton function $\\lambda > 0$, and $m > 1$, where the coefficient $\\mu= 1/m$ is constant. We introduce the weighted function $v = e^{-f/m}\\lambda$ and prove it is subharmonic. This leads to five rigidity results, each forcing the manifold to be Euclidean. We first show by a concrete example that if $\\mu$ is allowed to be nonconstant, the rigidity conclusions fail even when all other hypotheses are satisfied. Therefore the constant mu condition is essential."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06129","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.06129/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}