{"paper":{"title":"Astheno-K\\\"ahler and balanced structures on fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Anna Fino, Gueo Grantcharov, Luigi Vezzoni","submitted_at":"2016-08-24T08:22:18Z","abstract_excerpt":"We study the existence of three classes of Hermitian metrics on certain types of compact complex manifolds. More precisely, we consider balanced, SKT and astheno-K\\\"ahler metrics. We prove that the twistor spaces of compact hyperk\\\"ahler and negative quaternionic-K\\\"ahler manifolds do not admit astheno-K\\\"ahler metrics. Then we provide examples of astheno-K\\\"ahler structures on toric bundles over K\\\"ahler manifolds. In particular, we find examples of compact complex non-K\\\"ahler manifolds which admit a balanced and an astheno-K\\\"ahler metrics, thus answering to a question in [52] (see also [24"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06743","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"}