{"paper":{"title":"Volume minimization and Conformally K\\\"ahler, Einstein-Maxwell geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Akito Futaki, Hajime Ono","submitted_at":"2017-06-24T13:32:18Z","abstract_excerpt":"Let $M$ be a compact complex manifold admitting a K\\\"ahler structure. A conformally K\\\"ahler, Einstein-Maxwell metric (cKEM metric for short) is a Hermitian metric $\\tilde{g}$ on $M$ with constant scalar curvature such that there is a positive smooth function $f$ with $g = f^2 \\tilde{g}$ being a K\\\"ahler metric and $f$ being a Killing Hamiltonian potential with respect to $g$. Fixing a K\\\"ahler class, we characterize such Killing vector fields whose Hamiltonian function $f$ with respect to some K\\\"ahler metric $g$ in the fixed K\\\"ahler class gives a cKEM metric $\\tilde{g} = f^{-2}g$. The chara"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07953","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"}