Geometry of the Cassinian Metric and Its Inner Metric

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• 作者：Zair Ibragimov ; Manas Ranjan Mohapatra…
• 关键词：Möbius transformation ; The hyperbolic metric ; The Cassinian metric ; The distance ratio metric ; The visual angle metric ; Inner metric
• 刊名：Bulletin of the Malaysian Mathematical Sciences Society
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：40
• 期：1
• 页码：361-372
• 全文大小：
• 刊物类别：Mathematics, general; Applications of Mathematics;
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Singapore
• ISSN：2180-4206
• 卷排序：40

文摘

The Cassinian metric and its inner metric have been studied for subdomains of the n-dimensional Euclidean space \({\mathbb {R}}^n\) (\(n\ge 2\)) by the first named author. In this paper we obtain various inequalities between the Cassinian metric and other related metrics in some specific subdomains of \({\mathbb {R}}^n\). Also, a sharp distortion property of the Cassinian metric under Möbius transformations of the unit ball is obtained.