A characterization of Möbius transformations by use of hyperbolic regular polygons

Demirel, Oğuzhan; Seyrantepe, Emine Soytürk

doi:10.1016/j.jmaa.2010.08.049

Cited by 6 publications

(3 citation statements)

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“…To see the characteristics of Möbius transformations involving Lambert quadrilaterals and Saccheri quadrilaterals, we refer the reader to [4]. Moreover, there are many characterizations of Möbius transformations by using various hyperbolic polygons; see, for instance, [5][6][7].…”

Section: De Nition 3 [3]mentioning

confidence: 99%

The hyperbolic polygons of type (ϵ, n) and Möbius transformations

Demirel

2020

Open Mathematics

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Abstract An n-sided hyperbolic polygon of type (ϵ, n) is a hyperbolic polygon with ordered interior angles $\begin{array}{} \frac{\pi}{2} \end{array} $ + ϵ, θ1, θ2, …, θn−2, $\begin{array}{} \frac{\pi}{2} \end{array} $ − ϵ, where 0 < ϵ < $\begin{array}{} \frac{\pi}{2} \end{array} $ and 0 < θi < π satisfying $$\begin{array}{} \displaystyle \sum_{i = 1}^{n-2} \theta_{i}+\Big(\frac{\pi}{2}+\epsilon\Big)+\Big(\frac{\pi}{2}-\epsilon\Big) \lt (n-2)\pi \end{array} $$ and θi + θi+1 ≠ π (1 ≤ i ≤ n − 3), θ1 + ( $\begin{array}{} \frac{\pi}{2} \end{array} $ + ϵ) ≠ π, θn−2 + ( $\begin{array}{} \frac{\pi}{2} \end{array} $ − ϵ) ≠ π. In this paper, we present a new characterization of Möbius transformations by using n-sided hyperbolic polygons of type (ϵ, n). Our proofs are based on a geometric approach.

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Section: De Nition 3 [3]mentioning

confidence: 99%

The hyperbolic polygons of type (ϵ, n) and Möbius transformations

Demirel

2020

Open Mathematics

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“…[3] The Saccheri quadrilateral is a hyperbolic quadrilateral with angles π 2 , π 2 , θ and θ, where 0 < θ < π 2 . To see other characterizations of Möbius transformations with the help of hyperbolic polygons, we refer [10], [5], [6] and [7].…”

Section: Introductionmentioning

confidence: 99%

Degenerate Saccheri Quadrilaterals, Möbius Transformations and Conjugate Möbius Transformations

Demirel¹

2017

International Electronic Journal of Geometry

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“…As for the geometric aspect, circle preserving is the most well known characterization of Möbius transformations. In addition to this, in literature, there are many characterizations of Möbius transformations via some hyperbolic polygons; see [1][2][3][4][5][6][7]. For other characterizations of hyperbolic isometries (in fact, these are Möbius transformations), we refer the reader to [8,9] and [10].…”

Section: Introductionmentioning

confidence: 99%