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

Let a and m be positive integers such that 2a < m. We show that in the domain $D:={z\in \u2102\xb3|r\left(z\right):=\Re z\u2081+|z\u2081|\xb2+|z\u2082|}^{2m}+{\left|z\u2082z\u2083\right|}^{2a}+{\left|z\u2083\right|}^{2m}<0$ 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.