{"paper":{"title":"Pure spinors, intrinsic torsion and curvature in odd dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Arman Taghavi-Chabert","submitted_at":"2013-04-03T19:57:34Z","abstract_excerpt":"We study the geometric properties of a $(2m+1)$-dimensional complex manifold $\\mathcal{M}$ admitting a holomorphic reduction of the frame bundle to the structure group $P \\subset \\mathrm{Spin}(2m+1,\\mathbb{C})$, the stabiliser of the line spanned by a pure spinor at a point. Geometrically, $\\mathcal{M}$ is endowed with a holomorphic metric $g$, a holomorphic volume form, a spin structure compatible with $g$, and a holomorphic pure spinor field $\\xi$ up to scale. The defining property of $\\xi$ is that it determines an almost null structure, i.e.\\ an $m$-plane distribution $\\mathcal{N}_\\xi$ alon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1076","kind":"arxiv","version":3},"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"}