{"paper":{"title":"Einstein $\\mathrm{SU}(3)$ and $\\mathrm{G}_2$ structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"V\\'ictor Manero","submitted_at":"2016-07-26T16:10:05Z","abstract_excerpt":"We describe a method to obtain $\\mathrm{SU}(3)$-structures and $\\mathrm{G}_2$-structures on 6 and 7-dimensional manifolds respectively, such that its associated metric is Einstein. More concretely, we have that different classes of $\\mathrm{SU}(2)$ and $\\mathrm{SU}(3)$-structures, on 5 and 6-dimensional manifolds whose induced metric is Einstein can produce, via warped products, different classes $\\mathrm{SU}(3)$ and $\\mathrm{G}_2$-structures such that its associated metric is also Einstein."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07775","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"}