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Counterexamples related to the Kobayashi Pseudodistance

2022/09/13 by Winkelmann, Joerg
Mathematics · #32Q45 #Advanced Algebra and Geometry #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2209.06281

openalex publication_date 2022/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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