{"paper":{"title":"Geometric structures of vectorial type","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ilka Agricola, Thomas Friedrich (HU Berlin)","submitted_at":"2005-09-07T08:56:23Z","abstract_excerpt":"We study geometric structures of $\\mathcal{W}_4$-type in the sense of A. Gray on a Riemannian manifold. If the structure group $\\mathrm{G} \\subset \\SO(n)$ preserves a spinor or a non-degenerate differential form, its intrinsic torsion $\\Gamma$ is a closed 1-form (Proposition \\ref{dGamma} and Theorem \\ref{Fixspinor}). Using a $\\mathrm{G}$-invariant spinor we prove a splitting theorem (Proposition \\ref{splitting}). The latter result generalizes and unifies a recent result obtained in \\cite{Ivanov&Co}, where this splitting has been proved in dimensions $n=7,8$ only. Finally we investigate geometr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509147","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"}