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.