Extremal metrics on Hartogs domains

2007/05/15 by Andrea Loi, Loi, Andrea, Fabio Zuddas +1
Mathematics · #32Q15 #32T15 #53C55 #Advanced Algebra and Geometry #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0705.2124

openalex publication_date 2007/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An n-dimensional Hartogs domain D_F with strongly pseudoconvex boundary can be equipped with a natural \K metric g_F. In this paper we prove that if g_F is an extremal \K metric then (D_F, g_F) is biholomorphically isometric to the n-dimensional complex hyperbolic space.

Related

• Canonical metrics on Hartogs domains
• Riemannian geometry of Hartogs domains
• Kähler geometry of bounded pseudoconvex Hartogs domains
• Remarks on the canonical metrics on the Cartan-Hartogs domains
• The Kobayashi metric, extremal discs, and biholomorphic mappings