{"paper":{"title":"On Homogeneous K\\\"ahler Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Antonio De Nicola, Fabrizio Pugliese, Luca Vitagliano","submitted_at":"2026-08-04T15:04:56Z","abstract_excerpt":"The cone $M \\times \\mathbb{R}_+$ over a Sasakian manifold $M$ is equipped with a canonical K\\\"ahler structure with specific homogeneity properties with respect to the $\\mathbb{R}_+$ coordinate. This K\\\"ahler structure completely encodes the underlying Sasakian structure. Recently, Grabowski, Grabowska and Mohseni provided a broader conceptual framework for this phenomenon via homogeneous K\\\"ahler structures, i.e. K\\\"ahler structures on a principal $\\mathbb{R}^\\times$-bundle $P$ satisfying similar homogeneity properties. This approach successfully extends Sasakian geometry from cooriented conta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03785","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.03785/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}