{"paper":{"title":"Bi-conformal vector fields and their applications to the characterization of conformally separable pseudo-Riemannian manifolds: New criteria for the existence of conformally flat foliations in pseudo-Riemannian manifolds","license":"","headline":"","cross_cats":["gr-qc","math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Alfonso Garc\\'ia-Parrado G\\'omez-Lobo","submitted_at":"2004-09-17T16:29:05Z","abstract_excerpt":"In this paper 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. Bi-conformal vector fields are defined on a pseudo-Riemannian manifold through the differential conditions $\\lie P_{ab}=\\phi P_{ab}$ and $\\lie\\Pi_{ab}=\\chi\\Pi_{ab}$ where $P_{ab}$ and $\\Pi_{ab}$ are orthogonal and complementary projectors with respect to the metric tensor $\\rmg_{ab}$. One o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0409037","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"}