{"paper":{"title":"The complex Goldberg-Sachs theorem in higher dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-th","math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Arman Taghavi-Chabert","submitted_at":"2011-07-12T13:33:03Z","abstract_excerpt":"We study the geometric properties of holomorphic distributions of totally null $m$-planes on a $(2m+\\epsilon)$-dimensional complex Riemannian manifold $(\\mathcal{M}, \\bm{g})$, where $\\epsilon \\in {0,1}$ and $m \\geq 2$. In particular, given such a distribution $\\mathcal{N}$, say, we obtain algebraic conditions on the Weyl tensor and the Cotton-York tensor which guarrantee the integrability of $\\mathcal{N}$, and in odd dimensions, of its orthogonal complement. These results generalise the Petrov classification of the (anti-)self-dual part of the complex Weyl tensor, and the complex Goldberg-Sach"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2283","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"}