Bergman representative coordinates on the Siegel-Jacobi disk

2014/09/01 by Stefan Berceanu, Berceanu, Stefan
Mathematics · #32Q15 #57Q35 #81R30 #81S10 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1409.0368

openalex publication_date 2014/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We underline some differences between the geometric aspect of Berezin's approach to quantization on homogeneous Kähler manifolds and Bergman's construction for bounded domains in ℂⁿ. We construct explicitly the Bergman representative coordinates for the Siegel-Jacobi disk D^J₁, which is a partially bounded manifold whose points belong to ℂ\timesD₁, where D₁ denotes the Siegel disk. The Bergman representative coordinates on D^J₁ are globally defined, the Siegel-Jacobi disk is a normal Kähler homogeneous Lu Qi-Keng manifold, whose representative manifold is the Siegel-Jacobi disk itself.

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