On the Generalized Poincare Distance

Yıl 2023, Cilt: 5 Sayı: 2 , 1 - 5 , 30.12.2023

Ayşe Bayar , Sezin Cirdi Şaan

https://izlik.org/JA64ZC68PS

Öz

In this work, the concept of the generalized Poincaré distance is given and the distance between two points on vertical lines, horizontal lines and semi-ellipses in the upper half-plane are examined. It is also shown that translations parallel to the x-axis and reflections in the vertical lines preserve the generalized Poincaré distance in the upper half-plane.

Anahtar Kelimeler

Poincare distance , the upper half-plane , hyperbolic plane

Kaynakça

• Stahl, S. (1993). The Poincare half-plane: A Gateway to modern geometry. Jones & Bartlett Learning.
• Anderson, J. W. (2005). Hyperbolic geometry. Springer Undergraduate Mathematics Series, Springer-Verlag. https://doi.org/10.1007/1-84628-220-9
• Greenberg, M. J. (1993). Euclidean and non-Euclidean geometries: Development and history. Macmillan.
• Kaya, R. (2022). Generalized Poincare half-planes. arXiv preprint, arXiv:1904.01899. https://doi.org/10.48550/arXiv.1904.01899.
• Bayar, A., Ekmekçi, S., & Akça, Z. (2008). On the plane geometry with generalized absolute value metric. Mathematical Problems in Engineering, Article ID 673275, 1-8.
• Çolakoglu, H. B., & Kaya, R. (2011). A generalization of some well-known distances and related isometries. Mathematical Communications, 16(1), 21-35.
• Ekmekçi, S., Bayar, A., & Altıntaş, A. K. (2015). On the group of isometries of the generalized taxicab plane. International Journal of Contemporary Mathematical Sciences, 10(4), 159-166.
• Ekmekçi, S., Akça, Z., & Altıntaş, K. (2015). On trigonometric functions and norm in the generalized taxicab metric Mathematical Sciences and Applications E-Notes, 3(2), 27-33.
• Kaya, R., Gelişgen, Ö., Ekmekçi, S., & Bayar, A. (2009). On the group of isometries of the plane with generalized absolute value metric. The Rocky Mountain Journal of Mathematics, 39(2), 591-603.