The cogyrolines of M?bius gyrovector spaces are metric but not periodic

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• 作者：O?uzhan Demirel (1)
  Emine Soytürk Seyrantepe (1)
  
• 关键词：39B42 ; 51M05 ; 51M10 ; 51M25 ; 30F45 ; Metric spaces ; functional equations of metric and periodic lines and their solutions ; Poincaré ball model of hyperbolic geometry ; M?bius gyrovector space
• 刊名：Aequationes Mathematicae
• 出版年：2013
• 出版时间：2 - March 2013
• 年：2013
• 卷：85
• 期：1
• 页码：185-200
• 全文大小：317KB
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• 作者单位：O?uzhan Demirel (1)
  Emine Soytürk Seyrantepe (1)
  
  1. Department of Mathematics, Faculty of Science and Arts, ANS Campus, Afyon Kocatepe University, 03200, Afyonkarahisar, Turkey
  
• ISSN：1420-8903

文摘

In this paper, we prove that every metric line of a M?bius gyrovector space ${(\mathbb{R}_{1}^{n}, \oplus, \otimes)}$ is exactly a cogyroline of itself, and also we prove the nonexistence of periodic lines in ${(\mathbb{R}_{1}^{n}, \oplus, \otimes)}$ .