{"paper":{"title":"Bi-conformal vector fields and the local geometric characterization of conformally separable (double-twisted) pseudo-Riemannian manifolds","license":"","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Alfonso Garc\\'ia-Parrado G\\'omez-Lobo","submitted_at":"2005-04-08T07:20:58Z","abstract_excerpt":"This is the first of two companion papers in which a thorough study of the normal form and the first integrability conditions arising from {\\em bi-conformal vector fields} is presented. These new symmetry transformations were introduced in {\\em Class. Quantum Grav.} \\textbf{21}, 2153-2177 and some of their basic properties were addressed there. In our calculations a new affine connection ({\\em bi-conformal connection}) arises quite naturally and this connection enables us to find a local characterization of {\\em conformally separable} pseudo-Riemannian manifolds (also called double twisted pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504162","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"}