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Injective hyperbolicity of domains. (English) Zbl 0847.32027

Let \(K_D\) denote the Kobayashi-Royden pseudometric on a domain \(D\) in \(\mathbb{C}^n\), and let \(S_D\) denote the pseudometric defined by K. T. Hahn [Ann. Pol. Math. 39, 71-81 (1981; Zbl 0476.32031)] using injective holomorphic mappings. In contrast to the situation for \(n = 1\) where \(K_D = S_D\) if and only if \(D\) is simply connected, the author proves that for \(n \geq 3\) the pseudometrics \(K_D\) and \(S_D\) always coincide.

MSC:

32F45 Invariant metrics and pseudodistances in several complex variables

Citations:

Zbl 0476.32031
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