Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 064, 28 pages      arXiv:1512.00601

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

Received March 03, 2016, in final form June 17, 2016; Published online June 27, 2016

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.

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

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