{"paper":{"title":"Doubrov-Ferapontov general heavenly equation and the hyper-K\\\"ahler hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math.DG"],"primary_cat":"nlin.SI","authors_text":"L. V. Bogdanov","submitted_at":"2014-12-23T14:36:38Z","abstract_excerpt":"We give a description of recently introduced Doubrov-Ferapontov general heavenly equation in terms of closed differential Pl\\\"ucker two-form, rationally depending on the spectral parameter. We demonstrate that general heavenly equation is an important generating equation in the context of Takasaki hyper-K\\\"ahler hierarchy, and it is also directly connected to hyper-K\\\"ahler geometry through the Gindikin construction. We develop a $\\bar{\\partial}$-dressing scheme and introduce a formula for the potential satisfying the general heavenly equation. Multidimensional generalization is also outlined."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7376","kind":"arxiv","version":2},"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"}