{"paper":{"title":"Naturally reductive pseudo-Riemannian Lie groups in low dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Francisco Vittone, Gabriela P. Ovando, Viviana del Barco","submitted_at":"2012-11-05T15:09:28Z","abstract_excerpt":"This work concerns the non-flat metrics on the Heisenberg Lie group of dimension three $\\Heis_3(\\RR)$ and the bi-invariant metrics on the solvable Lie groups of dimension four. On $\\Heis_3(\\RR)$ we prove that the property of the metric being naturally reductive is equivalent to the property of the center being non-degenerate. These metrics are Lorentzian algebraic Ricci solitons. We start with the indecomposable Lie groups of dimension four admitting bi-invariant metrics and which act on $\\Heis_3(\\RR)$ by isometries and we finally study some geometrical features on these spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0884","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"}