Geodesic
Kobayashi-Royden vs. Hahn pseudometric in ℂ²
Annales Polonici Mathematici, Tome 75 (2000) no. 3, pp. 289-294 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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For a domain D ⊂ ℂ the Kobayashi-Royden ϰ and Hahn h pseudometrics are equal iff D is simply connected. Overholt showed that for $D ⊂ ℂ^n$, n ≥ 3, we have $h_D ≡ ϰ_D$. Let D₁, D₂ ⊂ ℂ. The aim of this paper is to show that $h_{D₁ × D₂}$ iff at least one of D₁, D₂ is simply connected or biholomorphic to ℂ \ {0}. In particular, there are domains D ⊂ ℂ² for which $h_D ≢ ϰ_D$.
DOI : 10.4064/ap-75-3-289-294
Mots-clés : Hahn pseudometric, Kobayashi pseudometric

Witold Jarnicki 1

1 
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Witold Jarnicki. Kobayashi-Royden vs. Hahn pseudometric in ℂ². Annales Polonici Mathematici, Tome 75 (2000) no. 3, pp. 289-294. doi: 10.4064/ap-75-3-289-294

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