INJECTIVE HYPERBOLICITY OF PRODUCT DOMAIN

Choi, Ki-Seong; Choi, Ki-Seong

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P-ISSN3059-0604
E-ISSN3059-1309
KCI

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Vol.5 No.1

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Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309

1998, v.5 no.1, pp.73-78

Choi, Ki-Seong

Choi,, K. (1998). , 5(1), 73-78.

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Abstract

Let $H_1$ ($\Delta$, M) be the family of all 1-1 holomorphic mappings of the unit disk $\Delta\; \subset\; C$ into a complex manifold M. Following the method of Royden, Hahn introduces a new pseudo-differential metric $S_{M}$ on M. The present paper is to study the product property of the metric $S_{M}$ when M is given by the product of two domains $D_1$ and $D_2$ in the complex plane C, thus investigating the hyperbolicity of the product domain $D_1 \;\times\; D_2$ with respect to $S_{M}$ metric.

keywords: Kobayashi-Royden metric, S-metric

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Article Contents

Vol.5 No.1

Abstract

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics