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Is There Any Metric Line Which Can Be Represented By A Single Fixed Point?

Year 2019, , 54 - 62, 27.06.2019
https://doi.org/10.33484/sinopfbd.469669

Abstract

In this paper, determining metric lines in Levenberg plane, a special metric line example which can be written by using a single fixed point is presented. Moreover, we prove nonexistence of periodic lines in Levenberg plane and give a problem whether there exist a distance space in which periodic lines written by using a single fixed point?

References

  • [1] Benz, W., Metric and periodic lines in real inner product space geometries. Monatsh. Math.141 (2004), no. 1, 1–10.
  • [2] Benz, W., Classical Geometries in Modern Contexts, Birkhauser, 2007.
  • [3] Blumenthal LM, Menger K (1970) Studies in Geometry. San Francisco: Freeman.
  • [4] Demirel, O., Seyrantepe E.S, Sönmez, N., Metric and periodic lines in the Poincare ball modelof hyperbolic geometry, Bull. Iran. Math. Soc. 38 (2012), no. 3, 805–815.
  • [5] Demirel, O., Seyrantepe E.S, The cogyrolines of Möbius gyrovector spaces are metric but notperiodic, Aequationes Math. 85 (2013), no. 1-2, 185–200.
  • [6] Gelisgen, O., On the Congruence of Triangles in Levenberg Plane, Dumlupinar ¨ Universitesi ¨Fen Bilimleri Enstitüsü 14, 2007.
  • [7] Höfer, R., Metric lines in Lorentz-Minkowski geometry, Aequationes Math. 71 (2006), no. 1-2,162–173.
  • [8] Höfer, R., Metric and Periodic lines in de Sitter’s World, J.Geom. 90 (2008), 66–82.
Year 2019, , 54 - 62, 27.06.2019
https://doi.org/10.33484/sinopfbd.469669

Abstract

References

  • [1] Benz, W., Metric and periodic lines in real inner product space geometries. Monatsh. Math.141 (2004), no. 1, 1–10.
  • [2] Benz, W., Classical Geometries in Modern Contexts, Birkhauser, 2007.
  • [3] Blumenthal LM, Menger K (1970) Studies in Geometry. San Francisco: Freeman.
  • [4] Demirel, O., Seyrantepe E.S, Sönmez, N., Metric and periodic lines in the Poincare ball modelof hyperbolic geometry, Bull. Iran. Math. Soc. 38 (2012), no. 3, 805–815.
  • [5] Demirel, O., Seyrantepe E.S, The cogyrolines of Möbius gyrovector spaces are metric but notperiodic, Aequationes Math. 85 (2013), no. 1-2, 185–200.
  • [6] Gelisgen, O., On the Congruence of Triangles in Levenberg Plane, Dumlupinar ¨ Universitesi ¨Fen Bilimleri Enstitüsü 14, 2007.
  • [7] Höfer, R., Metric lines in Lorentz-Minkowski geometry, Aequationes Math. 71 (2006), no. 1-2,162–173.
  • [8] Höfer, R., Metric and Periodic lines in de Sitter’s World, J.Geom. 90 (2008), 66–82.
There are 8 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Articles
Authors

Oğuzhan Demirel

Publication Date June 27, 2019
Submission Date October 11, 2018
Published in Issue Year 2019

Cite

APA Demirel, O. (2019). Is There Any Metric Line Which Can Be Represented By A Single Fixed Point?. Sinop Üniversitesi Fen Bilimleri Dergisi, 4(1), 54-62. https://doi.org/10.33484/sinopfbd.469669


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