{"paper":{"title":"Hodge theory on nearly Kaehler manifolds","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["hep-th","math.AG"],"primary_cat":"math.DG","authors_text":"Misha Verbitsky","submitted_at":"2005-10-28T03:02:11Z","abstract_excerpt":"Let (M,I, \\omega, \\Omega) be a nearly Kaehler 6-manifold, that is, an SU(3)-manifold with the (3,0)-form \\Omega and the Hermitian form \\omega which satisfies $d\\omega=3\\lambda\\Re\\Omega, d\\Im\\Omega=-2\\lambda\\omega^2$, for a non-zero real constant \\lambda. We develop an analogue of Kaehler relations on M, proving several useful identities for various intrinsic Laplacians on M. When M is compact, these identities bring powerful results about cohomology of M. We show that harmonic forms on M admit the Hodge decomposition, and prove that H^{p,q}(M)=0 unless p=q or (p=1, q=2) or (p=2, q=1)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510618","kind":"arxiv","version":8},"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"}