Balanced Metric and Berezin Quantization on the Siegel-Jacobi Ball

2015/12/31 by Stefan Berceanu
Engineering · Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algorithm #Ball (mathematics) #Engineering #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical analysis #Mathematics #Metric (unit) #Pure mathematics #Quantization (signal processing) #Siegel modular form #math.DG #msc:32Q15 #msc:53D50 #msc:57Q35 #msc:81R30 #msc:81S10

paper · pdf · doi:10.3842/sigma.2016.064

published as SIGMA 12 (2016), 064, 28 pages

arxiv created 2016/06/27 · openalex publication_date 2016/06/27 · arxiv updated 2016/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We determine the matrix of the balanced metric of the Siegel-Jacobi ball and its inverse. We calculate the scalar curvature, the Ricci form and the Laplace-Beltrami operator of this manifold. We discuss several geometric aspects related with Berezin quantization on the Siegel-Jacobi ball.

Citations

• Lectures on Kähler Geometry
• Bergman representative coordinates on the Siegel-Jacobi disk
• Scalar Curvature and Projective Embeddings, I
• Realization of coherent state Lie algebras by differential operators
• Differential Geometry, Lie Groups, and Symmetric Spaces
• Invariant metrics and Laplacians on Siegel–Jacobi space
• Invariant Affine Connections on Homogeneous Spaces
• Isometric Imbedding of Complex Manifolds
• Symplectic Geometry
• Riemannian Geometry and Geometric Analysis