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Kobayashi-Royden vs. Hahn pseudometric in ℂ²

Witold Jarnicki — 2000

Annales Polonici Mathematici

For a domain D ⊂ ℂ the Kobayashi-Royden ϰ and Hahn h pseudometrics are equal iff D is simply connected. Overholt showed that for D n , n ≥ 3, we have h D ϰ D . Let D₁, D₂ ⊂ ℂ. The aim of this paper is to show that h D × D iff at least one of D₁, D₂ is simply connected or biholomorphic to ℂ 0. In particular, there are domains D ⊂ ℂ² for which h D ϰ D .

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