{"paper":{"title":"Harmonic morphisms and moment maps on hyper-K\\\"ahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"E. Loubeau, M. Benyounes, R. Pantilie","submitted_at":"2013-04-18T06:16:54Z","abstract_excerpt":"We characterise the actions, by holomorphic isometries on a K\\\"ahler manifold with zero first Betti number, of an abelian Lie group of dim\\geq 2, for which the moment map is horizontally weakly conformal (with respect to some Euclidean structure on the Lie algebra of the group). Furthermore, we study the hyper-K\\\"ahler moment map $\\phi$ induced by an abelian Lie group T acting by triholomorphic isometries on a hyper-K\\\"ahler manifold M, with zero first Betti number, thus obtaining the following: If dim T=1 then $\\phi$ is a harmonic morphism. Moreover, we illustrate this on the tangent bundle o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5028","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"}