An example of a pseudoconvex domain whose holomorphic sectional curvature of the Bergman metric is unbounded
Annales Polonici Mathematici, Tome 92 (2007) no. 1, pp. 29-39.

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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.
DOI : 10.4064/ap92-1-3
Keywords: positive integers domain bbb holomorphic sectional curvature x bergman metric direction tends infty tends non tangentially direction suitably chosen seems example feature has known far

Gregor Herbort 1

1 Bergische Universität Wuppertal Fachbereich C – Mathematik und Naturwissenschaften Gaußstraße 20 D-42097 Wuppertal, German
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Gregor Herbort. An example of a pseudoconvex domain whose holomorphic 
 sectional curvature of the
 Bergman metric is unbounded. Annales Polonici Mathematici, Tome 92 (2007) no. 1, pp. 29-39. doi : 10.4064/ap92-1-3. http://geodesic.mathdoc.fr/articles/10.4064/ap92-1-3/

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