This article is cited in 9 papers

Balanced Metric and Berezin Quantization on the Siegel–Jacobi Ball

Stefan Berceanu

National Institute for Physics and Nuclear Engineering, Department of Theoretical Physics, PO BOX MG-6, Bucharest-Magurele, Romania

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.

Keywords: Jacobi group; Siegel–Jacobi ball; balanced metric; homogenous Kähler manifolds; Laplace–Beltrami operator; scalar curvature; Ricci form; Berezin quantization.

MSC: 32Q15; 81S10; 53D50; 57Q35; 81R30

Received: March 3, 2016; in final form June 17, 2016; Published online June 27, 2016

Language: English

DOI: 10.3842/SIGMA.2016.064

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ArXiv: 1512.00601