{"paper":{"title":"Integrability of generalized structures on odd exact Courant algebroids using generalized connections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Liana David, Marius Mirea, Vicente Cort\\'es","submitted_at":"2026-05-18T12:24:01Z","abstract_excerpt":"Odd exact Courant algebroids constitute a simple class of transitive Courant algebroids. Their underlying vector bundle is of odd rank and differs from a generalized tangent bundle by the addition of a line bundle. In this article we study natural analogues of almost complex and almost pseudo-Hermitian structures on such Courant algebroids, which are called B_n-generalized almost complex/pseudo-Hermitian structures. The corresponding integrable structures are known as B_n-generalized complex structures and B_n-generalized pseudo-K\\\"{a}hler structures, respectively. We characterize the integrab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18306","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.18306/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.204959Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T23:21:58.890270Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"6a256a56c90143009fa64d9a1d489a76d929643b32628d9fac345bd1db74428f"},"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"}