{"paper":{"title":"On the rigidity of special and exceptional geometries with torsion a closed $3$-form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.DG","authors_text":"Georgios Papadopoulos","submitted_at":"2025-11-25T18:04:02Z","abstract_excerpt":"Under some suitable assumptions Riemannian manifolds $(M, g, H)$ that admit a connection $\\hat\\nabla$ with torsion a 3-form $H$, which is both closed $d H=0$ and $\\hat\\nabla$-covariantly constant, are locally isometric to a product $N\\times G$, where $G$ is a semisimple group and $N$ is a Riemannian manifold with $H\\vert_N=0$. If $M$ is simply connected and complete, then by the de Rham theorem $M=N\\times G$ globally. We use this to simplify the proof of similar results for strong CYT and HKT manifolds that obey the above hypotheses and extend them to strong $G_2$ and $\\mathrm{Spin}(7)$ manifo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.20568","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.20568/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}