Kobayashi-Royden vs. Hahn pseudometric in \Bbb C²

2000/09/30 by Witold Jarnicki
Mathematics · #math.CV #msc:32F45

paper · pdf

published as Ann. Polon. Math. 75 (2000), 289-294. · 5 pages

arxiv created 2000/10/24 · arxiv updated 2009/11/30

Abstract

For a domain D⊂\Bbb C the Kobayashi--Royden κ and Hahn h pseudometrics are equal iff D is simply connected. Overholt showed that for D⊂\Bbb Cⁿ, n≥3, we have h_D≡κ_D. Let D₁,D₂⊂\Bbb C. The aim of this paper is to show that h_{D1× D2}≡κ_{D1× D2} iff at least one of D₁, D₂ is simply connected or biholomorphic to \Bbb C∖\0\. In particular, there are domains D⊂\Bbb C² for which h_D\not≡κ_D.

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