{"paper":{"title":"A local characterization for constant curvature metrics in 2-dimensional Lorentz manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alexandre Lymberopoulos, Ivo Terek","submitted_at":"2016-05-24T18:28:17Z","abstract_excerpt":"In this paper we define Fermi-type coordinates in a 2-dimensional Lorentz manifold, and use this coordinate system to provide a local characterization of constant Gaussian curvature metrics for such manifolds, following a classical result from Riemann. We then exhibit particular isometric immersions of such metrics in the pseudo-Riemannian ambients L^3 (i.e., usual Lorentz-Minkowski space) and R^3_2 (i.e., R^3 endowed with an index 2 flat metric)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07573","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"}