{"paper":{"title":"Some remarks on Calabi-Yau and hyper-K\\\"ahler foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Georges Habib, Luigi Vezzoni","submitted_at":"2013-06-21T14:49:10Z","abstract_excerpt":"We study Riemannian foliations whose transverse Levi-Civita connection $\\nabla$ has special holonomy. In particular, we focus on the case where $Hol(\\nabla)$ is contained either in SU(n) or in Sp(n). We prove a Weitzenbock formula involving complex basic forms on K\\\"ahler foliations and we apply this formula for pointing out some properties of transverse Calabi-Yau structures. This allows us to prove that links provide examples of compact simply-connected contact Calabi-Yau manifolds. Moreover, we show that a simply-connected compact manifold with a K\\\"ahler foliation admits a transverse hyper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5159","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"}