{"paper":{"title":"Spinors and the Weyl Tensor Classification in Six Dimensions","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["hep-th","math.DG"],"primary_cat":"gr-qc","authors_text":"Bruno Carneiro da Cunha, Carlos Batista","submitted_at":"2012-12-12T02:12:44Z","abstract_excerpt":"A spinorial approach to 6-dimensional differential geometry is constructed and used to analyze tensor fields of low rank, with special attention to the Weyl tensor. We perform a study similar to the 4-dimensional case, making full use of the SO(6) symmetry to uncover results not easily seen in the tensorial approach. Using spinors, we propose a classification of the Weyl tensor by reinterpreting it as a map from 3-vectors to 3-vectors. This classification is shown to be intimately related to the integrability of maximally isotropic subspaces, establishing a natural framework to generalize the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2689","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"}