{"paper":{"title":"New K\\\"ahler metric on quasifuchsian space and its curvature properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Genkai Zhang, Inkang Kim, Xueyuan Wan","submitted_at":"2019-02-12T18:01:14Z","abstract_excerpt":"Let $QF(S)$ be the quasifuchsian space of a closed surface $S$ of genus $g\\geq 2$. We construct a new mapping class group invariant K\\\"ahler metric on $QF(S)$. It is an extension of the Weil-Petersson metric onthe Teichm\\\"uller space $\\mathcal T(S)\\subset QF(S)$. We also calculate its curvature and prove some negativity for the curvature along the tautological directions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.04523","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"}