Curvatures and invariant functions. (English) Zbl 0661.32004
The author studies a class of Kähler metrics invariant under the group of holomorphic automorphisms of the Reinhardt domain \(\{(z,w):| z|^{2p}+| w|^ 2<1\}\), where \(z\in {\mathbb{C}}\), \(w\in {\mathbb{C}}^ n\), and \(p\neq 1\). Ordinary differential equations are derived that determine such metrics satisfying various conditions on the Ricci curvature, scalar curvature, or holomorphic sectional curvature.
Reviewer: H.Boas
MSC:
32A07 | Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010) |
32F45 | Invariant metrics and pseudodistances in several complex variables |
53C55 | Global differential geometry of Hermitian and Kählerian manifolds |
32A25 | Integral representations; canonical kernels (Szegő, Bergman, etc.) |