{"paper":{"title":"The Abresch-Rosenberg Shape Operator and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Haimer A. Trejos, Jos\\'e M. Espinar","submitted_at":"2015-12-07T15:51:41Z","abstract_excerpt":"There exists a holomorphic quadratic differential defined on any $H-$ surface immersed in the homogeneous space $\\mathbb{E}(\\kappa,\\tau)$ given by U. Abresch and H. Rosenberg, called the Abresch-Rosenberg differential. However, there were no Codazzi pair on such $H-$surface associated to the Abresch-Rosenberg differential when $\\tau \\neq 0$. The goal of this paper is to find a geometric Codazzi pair defined on any $H-$surface in $\\mathbb{E}(\\kappa,\\tau)$, when $\\tau \\neq 0$, whose $(2,0)-$part is the Abresch-Rosenberg differential.\n  In particular, this allows us to compute a Simons' type form"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02099","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"}