{"paper":{"title":"Locally conformal calibrated $G_2$-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alberto Raffero, Anna Fino, Marisa Fern\\'andez","submitted_at":"2015-04-17T14:22:39Z","abstract_excerpt":"We study conditions for which the mapping torus of a 6-manifold endowed with an $SU(3)$-structure is a locally conformal calibrated $G_2$-manifold, that is, a 7-manifold endowed with a $G_2$-structure $\\varphi$ such that $d \\varphi = - \\theta \\wedge \\varphi$ for a closed non-vanishing 1-form $\\theta$. Moreover, we show that if $(M, \\varphi)$ is a compact locally conformal calibrated $G_2$-manifold with $\\mathcal{L}_{\\theta^{\\#}} \\varphi =0$, where ${\\theta^{\\#}}$ is the dual of $\\theta$ with respect to the Riemannian metric $g_{\\varphi}$ induced by $\\varphi$, then $M$ is a fiber bundle over $S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04508","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"}