{"paper":{"title":"Tanaka structures (non holonomic G-structures) and Cartan connections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dmitri V. Alekseevsky, Liana David","submitted_at":"2014-09-30T07:12:38Z","abstract_excerpt":"Let \\gh = \\gh_{-k}\\oplus \\cdots \\oplus \\gh_{l} (k >0, l \\geq 0) be a finite dimensional real graded Lie algebra, with a Euclidian metric \\langle \\cdot , \\cdot \\rangle adapted to the gradation. The metric \\langle\\cdot , \\cdot \\rangle is called admissible if the codifferentials \\partial^{*} : C^{k+1}(\\gh_{-}, \\gh ) \\ra C^{k} (\\gh_{-}, \\gh) (k\\geq 0) are Ad_{Q}-invariant (Lie(Q) = \\gh_{0}\\oplus \\gh_{+}). We find necessary and sufficient conditions for a Euclidian metric, adapted to the gradation, to be admissible, and we develop a theory of normal Cartan connections, when these conditions are sat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8405","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"}