{"paper":{"title":"Conformally K\\\"ahler geometry and quasi-Einstein metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ali Jizany, Stuart James Hall, Thomas Murphy, Wafaa Batat","submitted_at":"2015-02-25T11:57:40Z","abstract_excerpt":"We prove that the quasi-Einstein metrics found by L\\\"u, Page and Pope on $\\mathbb{C}P^{1}$-bundles over Fano K\\\"ahler-Einstein bases are conformally K\\\"ahler and that the K\\\"ahler class of the conformal metric is a multiple of the first Chern class. A detailed study of the lowest-dimensional example of such metrics on $\\mathbb{C}P^{2}\\sharp \\overline{\\mathbb{C}P}^{2}$ using the methods developed by Abreu and Guillemin for studying toric K\\\"ahler metrics is given. Our methods yield, in a unified framework, proofs of the existence of the Page, Koiso-Cao and L\\\"u-Page-Pope metrics on $\\mathbb{C}P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07140","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"}