On the Generalized Poincare Distance

Abstract

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.

Keywords

• Poincare distance
• the upper half-plane
• hyperbolic plane

References

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