{"paper":{"title":"Compact manifolds with positive $\\Gamma_2$-curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Boris Botvinnik, Mohammed Labbi","submitted_at":"2013-05-23T04:36:54Z","abstract_excerpt":"The Schouten tensor \\ $A$ \\ of a Riemannian manifold \\ $(M,g)$ provides important scalar curvature invariants $\\sigma_k$, that are the symmetric functions on the eigenvalues of $A$, where, in particular, $\\sigma_1$ \\ coincides with the standard scalar curvature \\ $\\Scal(g)$. Our goal here is to study compact manifolds with positive \\ $\\Gamma_2$-curvature, \\ i.e., when $\\sigma_1(g)>0$ and $\\sigma_2(g)>0$. In particular, we prove that a 3-connected non-string manifold $M$ admits a positive$\\Gamma_2$-curvature metric if and only if it admits a positive scalar curvature metric. Also we show that a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5313","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"}