Kähler geometry of bounded pseudoconvex Hartogs domains

2014/11/17 by Yihong Hao, An Wang, Hao, Yihong +1 · 2 citations
Mathematics · #32A07 #32Q15 #57R42 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1411.4447

openalex publication_date 2014/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Ω be a bounded pseudoconvex Hartogs domain. There exists a natural complete Kähler metric g^Ω in terms of its defining function. In this paper, we study two problems. The first one is determining when g^Ω is Einstein or extremal. The second one is the existence of holomorphic isometric immersions of (Ω, g^Ω) into finite or infinite dimensional complex space forms.

Cited by

• Bergman metrics induced by the ball
• Strongly not relatives Kaehler manifolds

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