Counterexamples related to the Kobayashi Pseudodistance
Complex Variables
2022-10-11 v2
Abstract
We present some unexpected examples related to the Kobayashi pseudodistance: For an unramified covering, the vanishing of the Kobayashi pseudodistance on the base does not imply the vanishing on the total space. The vanishing of the Kobayashi pseudodistance does not imply the vanishing of the Kobayashi Royden pseudo metric. Given a locally holomorphic trivial fiber bundle, the Kobayashi pseudodistance may vanish identically on the total space even if the fiber is hyperbolic.
Keywords
Cite
@article{arxiv.2209.06281,
title = {Counterexamples related to the Kobayashi Pseudodistance},
author = {Joerg Winkelmann},
journal= {arXiv preprint arXiv:2209.06281},
year = {2022}
}
Comments
11 pages, LaTeX. Some constructions have been made more explicit; references added