An example of a pseudoconvex domain whose holomorphic sectional curvature of the Bergman metric is unbounded
Volume 92 / 2007
Annales Polonici Mathematici 92 (2007), 29-39
MSC: 32F45, 32T25.
DOI: 10.4064/ap92-1-3
Abstract
Let $a$ and $m$ be positive integers such that $2a< m$. We show that in the domain $D:=\{ z\in \Bbb C^3\,|\, r(z):= \Re z_1 + |z_1|^2 + |z_2|^{2m} + |z_2z_3|^{2a}+|z_3|^{2m} <0\}$ the holomorphic sectional curvature $R_D(z;X)$ of the Bergman metric at $z$ in direction $X$ tends to $-\infty$ 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.
