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We extend and simplify results of \cite{Din~2009} where the asymptoticbehavior of the holomorphic sectional curvature of the Bergman metric in annuliis studied. Similarly as in \cite{Din~2009} the description enables us toconstruct an infinitely connected planar domain (in our paper it is a Zalcmantype domain) for which the supremum of the holomorphic sectional curvature istwo whereas its infimum is equal to $-\infty$.

Asymptotic behaviour of the sectional curvature of the Bergman metric for annuli