{"paper":{"title":"Conformally Einstein-Maxwell K\\\"ahler metrics and structure of the automorphism group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Akito Futaki, Hajime Ono","submitted_at":"2017-08-07T01:30:45Z","abstract_excerpt":"Let $(M,g)$ be a compact K\\\"ahler manifold and $f$ a positive smooth function such that its Hamiltonian vector field $K = J\\mathrm{grad}_g f$ for the K\\\"ahler form $\\omega_g$ is a holomorphic Killing vector field. We say that the pair $(g,f)$ is conformally Einstein-Maxwell K\\\"ahler metric if the conformal metric $\\tilde g = f^{-2}g$ has constant scalar curvature. In this paper we prove a reductiveness result of the reduced Lie algebra of holomorphic vector fields for conformally Einstein-Maxwell K\\\"ahler manifolds, extending the Lichnerowicz-Matsushima Theorem for constant scalar curvature K\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01958","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"}