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Invariant functions and invariant Kähler metrics on a class of Reinhardt domain. (Chinese. English summary) Zbl 0920.32003

Summary: Let \(\operatorname{Aut}(D)\) be the holomorphic automorphism group of the Reinhardt domain \(D\), \(D=\) \((k_1,k_2,\dots,k_p)\) \((1\leq p<n) \subset \mathbb{C}^n\). By using the invariant functions under \(\operatorname{Aut}(D)\), invariant Kähler metrics on \(D\) under \(\operatorname{Aut}(D)\) are given.

MSC:

32A07 Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)
32F45 Invariant metrics and pseudodistances in several complex variables
32M05 Complex Lie groups, group actions on complex spaces
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