• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.73-78
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• 1998

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.