An example for the holomorphic sectional curvature of the Bergman metric

Abstract

In this paper we study the behaviour of the holomorphic sectional curvature (or Gaussian curvature) of the Bergman metric of planar annuli. The results are then utilized to construct a domain for which the curvature is divergent at one of its boundary points and moreover the limes superior is the maximal possible for the Bergman metric (2), whereas the limes inferior is $-\infty$.