In this paper we prove that if a Ka ̈hler manifold (M, ω) admits a regular quantization then its scalar curvature is constant. Moreover, we apply this result to the two-dimensional complete Reinhardt domains in C2 to show that such domains admit a regular quantization iff they are biholomorphically isometric to the 2-ball in C2 endowed with the hyperbolic metric.
Regular quantizations of Kaehler manifolds and constant scalar curvature metrics
LOI, ANDREA
2005-01-01
Abstract
In this paper we prove that if a Ka ̈hler manifold (M, ω) admits a regular quantization then its scalar curvature is constant. Moreover, we apply this result to the two-dimensional complete Reinhardt domains in C2 to show that such domains admit a regular quantization iff they are biholomorphically isometric to the 2-ball in C2 endowed with the hyperbolic metric.
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