{"paper":{"title":"Spherical, hyperbolic and other projective geometries: convexity, duality, transitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrea Seppi, Fran\\c{c}ois Fillastre","submitted_at":"2016-11-03T15:31:52Z","abstract_excerpt":"Since the end of the 19th century, and after the works of F. Klein and H. Poincar\\'e, it is well known that models of elliptic geometry and hyperbolic geometry can be given using projective geometry, and that Euclidean geometry can be seen as a \"limit\" of both geometries. Then all the geometries that can be obtained in this way. Some of these geometries had a rich development, most remarkably hyperbolic geometry and the Lorentzian geometries of Minkowski, de Sitter and anti-de Sitter spaces, which in higher dimension have had large interest for a long time in mathematical physics and more prec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01065","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"}