An example for the holomorphic sectional curvature of the Bergman metric

Volume 98 / 2010

Żywomir Dinew Annales Polonici Mathematici 98 (2010), 147-167 MSC: Primary 32A36, 32W05; Secondary 32F45, 30A31, 30C40. DOI: 10.4064/ap98-2-4

Abstract

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 upper limit of the curvature at that point is maximal possible, equal to 2, whereas the lower limit is $-\infty $.

Authors

  • Żywomir DinewInstitute of Mathematics
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland
    e-mail

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