{"paper":{"title":"Hodge symmetry and decomposition on non-K\\\"ahler solvmanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Hisashi Kasuya","submitted_at":"2011-09-27T15:13:43Z","abstract_excerpt":"Let $G=\\C^{n}\\ltimes_{\\phi} \\C^{m}$ with a semi-simple action $\\phi: \\C^{n}\\to GL_{m}(\\C)$ (not necessarily holomorphic). Suppose $G$ has a lattice $\\Gamma$. Then we show that in some conditions on $G$ and $\\Gamma$, $G/\\Gamma$ admits a Hermitian metric such that the space of harmonic forms satisfies the Hodge symmetry and decomposition. By this result we give many examples of non-K\\\"ahler Hermitian solvmanifolds satisfying the Hodge symmetry and decomposition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5929","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":""},"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"}