{"paper":{"title":"Scalar curvature and the multiconformal class of a direct product Riemannian manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Nobuhiko Otoba, Saskia Roos","submitted_at":"2018-08-20T08:23:38Z","abstract_excerpt":"For a closed, connected direct product Riemannian manifold $(M, g)=(M_1\\times\\cdots\\times M_l, g_1\\oplus\\cdots\\oplus g_l)$, we define its multiconformal class $ [\\![ g ]\\!]$ as the totality $\\{f_1^2g_1\\oplus \\cdots\\oplus f_l^2g_l\\}$ of all Riemannian metrics obtained from multiplying the metric $g_i$ of each factor $M_i$ by a function $f_i^2>0$ on the total space $M$. A multiconformal class $ [\\![ g ]\\!]$ contains not only all warped product type deformations of $g$ but also the whole conformal class $[\\tilde{g}]$ of every $\\tilde{g}\\in [\\![ g ]\\!]$. In this article, we prove that $ [\\![ g ]\\!"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06340","kind":"arxiv","version":2},"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"}