{"paper":{"title":"Deformation of the $\\sigma_2$-curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Almir Silva Santos, Maria Andrade","submitted_at":"2018-01-02T12:42:06Z","abstract_excerpt":"Our main goal in this work is to deal with results concern to the $\\sigma_2$-curvature. First we find a symmetric 2-tensor canonically associated to the $\\sigma_2$-curvature and we present an Almost Schur Type Lemma. Using this tensor we introduce the notion of $\\sigma_2$-singular space and under a certain hypothesis we prove a rigidity result. Also we deal with the relations between flat metrics and $\\sigma_2$-curvature. With a suitable condition on the $\\sigma_2$-curvature we show that a metric has to be flat if it is close to a flat metric. We conclude this paper by proving that the 3-dimen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00628","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":""},"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"}