New Kähler metric on quasifuchsian space and its curvature properties

2019/02/12 by Инканг Ким, Xueyuan Wan, Kim, Inkang +3
Mathematics · #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1902.04523

openalex publication_date 2019/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let QF(S) be the quasifuchsian space of a closed surface S of genus g≥ 2. We construct a new mapping class group invariant Kähler metric on QF(S). It is an extension of the Weil-Petersson metric onthe Teichmüller space \mathcal T(S)⊂ QF(S). We also calculate its curvature and prove some negativity for the curvature along the tautological directions.

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