{"paper":{"title":"Weingarten type surfaces in $\\mathbb{H}^2\\times\\mathbb{R}$ and $\\mathbb{S}^2\\times\\mathbb{R}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Abigail Folha, Carlos Pe\\~nafiel","submitted_at":"2015-11-25T18:48:35Z","abstract_excerpt":"In this article, we study complete surfaces $\\Sigma$, isometrically immersed in the product space $\\mathbb{H}^2\\times\\mathbb{R}$ or $\\mathbb{S}^2\\times\\mathbb{R}$ having positive extrinsic curvature $K_e$. Let $K_i$ denote the intrinsic curvature of $\\Sigma$. Assume that the equation $aK_i+bK_e=c$ holds for some real constants $a\\neq0$, $b>0$ and $c$. The main result of this article state that when such a surface is a topological sphere it is rotational."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08146","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"}