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Aequationes mathematicae

, Volume 85, Issue 1–2, pp 185–200 | Cite as

The cogyrolines of Möbius gyrovector spaces are metric but not periodic

  • Oğuzhan Demirel
  • Emine Soytürk Seyrantepe
Article

Abstract

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

Mathematics Subject Classification

39B42 51M05 51M10 51M25 30F45 

Keywords

Metric spaces functional equations of metric and periodic lines and their solutions Poincaré ball model of hyperbolic geometry Möbius gyrovector space 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Science and Arts, ANS CampusAfyon Kocatepe UniversityAfyonkarahisarTurkey

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