On the Bergman representative coordinates

Abstract

We study the set where the so-called Bergman representative coordinates (or Bergman functions) form an immersion. We provide an estimate of the size of a maximal geodesic ball with respect to the Bergman metric, contained in this set. By concrete examples we show that these estimates are the best possible.

20 pages

References in corpus (2)

• An example for the holomorphic sectional curvature of the Bergman metric
• Asymptotic behaviour of the sectional curvature of the Bergman metric for annuli

Cited by in corpus (6)

• Bergman representative coordinates on the Siegel-Jacobi disk
• Coherent states and geometry on the Siegel-Jacobi disk
• Some remarks on the Kobayashi--Fuks metric on strongly pseudoconvex domains
• A differential-geometric analysis of the Bergman representative map
• Existence of geodesic spirals for the Kobayashi--Fuks metric on planar domains
• Weighted boundary limits of the Kobayashi--Fuks metric on h-extendible domains