{"paper":{"title":"Interior angle sums of geodesic triangles in $S^2 \\times R$ and $H^2 \\times R$ geometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Jen\\H{o} Szirmai","submitted_at":"2019-06-07T08:35:57Z","abstract_excerpt":"In the present paper we study $S^2 \\times R$ and $H^2 \\times R$ geometries, which are homogeneous Thurston 3-geometries. We analyse the interior angle sums of geodesic triangles in both geometries and prove, that in $S^2 \\times R$ space it can be larger or equal than $\\pi$ and in $H^2 \\times R$ space the angle sums can be less or equal than $\\pi$. In our work we will use the projective model of $S^2 \\times R$ and $H^2 \\times R$ geometries described by E. Moln\\'ar in \\cite{M97}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04037","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"}