{"paper":{"title":"G_2-structures on Einstein solvmanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Anna Fino, Marisa Fern\\'andez, Victor Manero","submitted_at":"2012-07-16T10:05:18Z","abstract_excerpt":"We study the $G_2$ analogue of the Goldberg conjecture on non-compact solvmanifolds. In contrast to the almost-K\\\"ahler case we prove that a 7-dimensional solvmanifold cannot admit any left-invariant calibrated $G_2$-structure $\\varphi$ such that the induced metric $g_{\\varphi}$ is Einstein, unless $g_{\\varphi}$ is flat. We give an example of 7-dimensional solvmanifold admitting a left-invariant calibrated $G_2$-structure $\\varphi$ such that $g_{\\varphi}$ is Ricci-soliton. Moreover, we show that a 7-dimensional (non-flat) Einstein solvmanifold $(S,g)$ cannot admit any left-invariant cocalibrat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3616","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"}