{"paper":{"title":"Constructing conformally invariant equations by using Weyl geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Sofiane Faci","submitted_at":"2012-12-11T19:51:13Z","abstract_excerpt":"We present a simple, systematic and practical method to construct conformally invariant equations in arbitrary Riemann spaces.\n  This method that we call \"Weyl-to-Riemann\" is based on two features of Weyl geometry. i) A Weyl space is defined by the metric tensor and the Weyl vector $W$, it becomes equivalent to a Riemann space when $W$ is gradient. ii) Any homogeneous differential equation written in a Weyl space by means of the Weyl connection is conformally invariant. The Weyl-to-Riemann method selects those equations whose conformal invariance is preserved when reducing to a Riemann space. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2599","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"}