{"paper":{"title":"Constant Angle Surfaces in Product Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Daniel Kowalczyk, Franki Dillen","submitted_at":"2011-05-04T12:59:53Z","abstract_excerpt":"We classify all the surfaces in $M^2(c_1)\\times M^2(c_2)$ for which the tangent space $T_pM^2$ makes constant angles with $T_p(M^2(c_1)\\times \\{p_2\\})$ (or equivalently with $T_p(\\{p_1\\}\\times M^2(c_2))$ for every point $p=(p_1,p_2)$ of $M^2$. Here $M^2(c_1)$ and $M^2(c_2)$ are 2-dimensional space forms, not both flat. As a corollary we give a classification of all the totally geodesic surfaces in $M^2(c_1)\\times M^2(c_2)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0813","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"}