An example of a pseudoconvex domain whose holomorphic sectional curvature of the Bergman metric is unbounded

• Autorzy: Gregor Herbort
• Języki publikacji: EN

Abstrakty

EN

Let a and m be positive integers such that 2a < m. We show that in the domain $D:= {z ∈ ℂ³ | r(z):= ℜ z₁ + |z₁|² + |z₂|^{2m} + |z₂z₃|^{2a} + |z₃|^{2m} <0}$ the holomorphic sectional curvature $R_D(z;X)$ of the Bergman metric at z in direction X tends to -∞ when z tends to 0 non-tangentially, and the direction X is suitably chosen. It seems that an example with this feature has not been known so far.

Kategorie tematyczne

• 32F45: Invariant metrics and pseudodistances
• 32T25: Finite type domains

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2007
• Tom: 92
• Numer: 1
• Strony: 29-39

Daty

wydano

2007

Twórcy

autor

Gregor Herbort

• Bergische Universität Wuppertal, Fachbereich C - Mathematik und Naturwissenschaften, Gaußstraße 20, D-42097 Wuppertal, German

Identyfikatory

DOI

10.4064/ap92-1-3