{"paper":{"title":"Twistor theory of hyper-K{\\\"a}hler metrics with hidden symmetries","license":"","headline":"","cross_cats":["gr-qc","hep-th","nlin.SI"],"primary_cat":"math.DG","authors_text":"Lionel J. Mason, Maciej Dunajski","submitted_at":"2003-01-16T14:54:50Z","abstract_excerpt":"We briefly review the hierarchy for the hyper-K\\\"ahler equations and define a notion of symmetry for solutions of this hierarchy. A four-dimensional hyper-K\\\"ahler metric admits a hidden symmetry if it embeds into a hierarchy with a symmetry. It is shown that a hyper-K\\\"ahler metric admits a hidden symmetry if it admits a certain Killing spinor. We show that if the hidden symmetry is tri-holomorphic, then this is equivalent to requiring symmetry along a higher time and the hidden symmetry determines a `twistor group' action as introduced by Bielawski \\cite{B00}. This leads to a construction fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0301171","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"}