{"paper":{"title":"Triangle angle sums related to translation curves in $\\SOL$ geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Jen\\H{o} Szirmai","submitted_at":"2017-03-20T09:44:55Z","abstract_excerpt":"After having investigated the geodesic and translation triangles and their angle sums in $\\NIL$ and $\\SLR$ geometries we consider the analogous problem in $\\SOL$ space that is one of the eight 3-dimensional Thurston geometries.\n  We analyse the interior angle sums of translation triangles in $\\SOL$ geometry and prove that it can be larger or equal than $\\pi$.\n  In our work we will use the projective model of $\\SOL$ described by E. Moln\\'ar in \\cite{M97},"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06646","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"}