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Quantization of Kähler manifolds. III. (English) Zbl 0826.53052

In two previous papers [J. Geom. Phys. 7, No. 1, 45-62 (1990; Zbl 0719.53044) and Trans. Am. Math. Soc. 337, No. 1, 73-98 (1993; Zbl 0788.53062)] the authors have examined various geometrical methods for the quantization of compact Kähler manifolds.
In the paper under review they make the first steps in extending these results to noncompact Kähler manifolds. As an example, the case of an open disk in \(\mathbb{C}\) with Poincaré metric is described in detail.

MSC:

53C55 Global differential geometry of Hermitian and Kählerian manifolds
53D50 Geometric quantization
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References:

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[2] Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A., and Sternheimer, D., Deformation theory and quantization,Ann. Phys. 111, 61–110 (1978). · Zbl 0377.53024 · doi:10.1016/0003-4916(78)90224-5
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[5] Cahen, M., Gutt, S., and Rawnsley, J., Quantization of Kähler manifolds. II,Trans. Amer. Math. Soc. 337, 73–98 (1993). · Zbl 0788.53062 · doi:10.2307/2154310
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