English

The Kobayashi metric for non-convex complex ellipsoids

Complex Variables 2009-09-25 v1

Abstract

In the paper we give some necessary conditions for a mapping to be a κ\kappa-geodesic in non-convex complex ellipsoids. Using these results we calculate explicitly the Kobayashi metric in the ellipsoids {z12+z22m<1}C2\{|z_1|^2+|z_2|^{2m}<1\}\subset\bold C^2, where m<12m<\frac12.

Cite

@article{arxiv.math/9407201,
  title  = {The Kobayashi metric for non-convex complex ellipsoids},
  author = {Peter Pflug and Wlodzimierz Zwonek},
  journal= {arXiv preprint arXiv:math/9407201},
  year   = {2009}
}
R2 v1 2026-07-22T17:54:55.997Z