{"paper":{"title":"Laplacian coflow for warped $\\mathrm{G}_2$-structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Antonio Otal, Raquel Villacampa, Victor Manero","submitted_at":"2019-04-12T07:38:10Z","abstract_excerpt":"We consider the Laplacian coflow of a $\\mathrm{G}_2$-structure on warped products of the form $M^7= M^6 \\times_f S^1$ with $M^6$ a compact 6-manifold endowed with an $\\mathrm{SU}(3)$-structure. We give an explicit reinterpretation of this flow as a set of evolution equations of the differential forms defining the $\\mathrm{SU}(3)$-structure on $M^6$ and the warping function $f$. Necessary and sufficient conditions for the existence of solution for this flow are given. Finally we describe new long time solutions for this flow where the $\\mathrm{SU}(3)$-structure on $M^6$ is nearly K\\\"ahler, symp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06080","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"}