{"paper":{"title":"Conformal immersion of Riemannian products in low codimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bruno Mendon\\c{c}a, Felippe Guimar\\~aes","submitted_at":"2018-11-13T23:37:19Z","abstract_excerpt":"We proved that a conformal immersion of $M_0^{n_0}\\times M_1^{n_1}$ as an hipersurface in a Euclidean space must be an extrinsic product of immersions, under the assumption that $n_0, n_1 \\geq 2$ and that $M^{n_0}_0\\times M^{n_1}_1$ is not conformally flat. We also stated a similar theorem for an arbitrary number of factors, more precisely, a conformal immersion $f\\colon M^{n_0}_0 \\times \\cdots \\times M^{n_k}_k \\rightarrow \\mathbb{R}^{n+k}$ must be an extrinsic product of immersions if one of the factors admits a plane with vanishing curvature and the remaining factors are not flat."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05570","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"}