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ISSN : 1226-0657

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Vol.5 No.1
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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
1998, v.5 no.1, pp.73-78
Choi, Ki-Seong
Choi,, K. (1998). . Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 5(1), 73-78.
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Abstract

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

keywords
Kobayashi-Royden metric, S-metric

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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