# Kobayashi-Royden vs. Hahn pseudometric in ℂ²

Annales Polonici Mathematici (2000)

- Volume: 75, Issue: 3, page 289-294
- ISSN: 0066-2216

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topWitold Jarnicki. "Kobayashi-Royden vs. Hahn pseudometric in ℂ²." Annales Polonici Mathematici 75.3 (2000): 289-294. <http://eudml.org/doc/208402>.

@article{WitoldJarnicki2000,

abstract = {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 $h_D ≢ ϰ_D$.},

author = {Witold Jarnicki},

journal = {Annales Polonici Mathematici},

keywords = {Hahn pseudometric; Kobayashi pseudometric},

language = {eng},

number = {3},

pages = {289-294},

title = {Kobayashi-Royden vs. Hahn pseudometric in ℂ²},

url = {http://eudml.org/doc/208402},

volume = {75},

year = {2000},

}

TY - JOUR

AU - Witold Jarnicki

TI - Kobayashi-Royden vs. Hahn pseudometric in ℂ²

JO - Annales Polonici Mathematici

PY - 2000

VL - 75

IS - 3

SP - 289

EP - 294

AB - 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 $h_D ≢ ϰ_D$.

LA - eng

KW - Hahn pseudometric; Kobayashi pseudometric

UR - http://eudml.org/doc/208402

ER -

## References

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