Remarks on Rawnsley's epsilon-function on the Fock-Bargmann-Hartogs domains

摘要

In this paper, we mainly study a family of unbounded non-hyperbolic domains in Cn+m, called Fock-Bargmann-Hartogs domains Dn,m() (>0) which are defined as a Hartogs type domains with the fiber over each zCn being a ball of radius e-z2. The purpose of this paper is twofold. Firstly, we obtain necessary and sufficient conditions for Rawnsley's epsilon-function epsilon(,g) of (Dn,m(),g(;)) to be a polynomial in 2, where g(;) is a Kahler metric associated with the Kahler potential z2-ln(e-z2-w2). Secondly, using above results, we study the Berezin quantization on Dn,m() with the metric g() (beta > 0).