Araştırma Makalesi
BibTex RIS Kaynak Göster

Degenerate Saccheri Quadrilaterals, Möbius Transformations and Conjugate Möbius Transformations

Yıl 2017, Cilt: 10 Sayı: 2, 32 - 36, 29.10.2017
https://doi.org/10.36890/iejg.545044

Öz

In this paper, we define a new geometric concept that we will call “degenerate Saccheri
quadrilateral” and use it to give a new characterization of Möbius transformations. Our proofs
are based on a geometric approach.

Kaynakça

  • [1] Aczél, J. and McKiernan, M.A., On the characterization of plane projective and complex Möbius transformations. Math. Nachr. 33, (1967), 315–337.
  • [2] Beardon, A.F. and Minda, D., Sphere-preserving maps in inversive geometry. Proc. Amer. Math. Soc. 130 (2002), no. 4, 987–998.
  • [3] Beardon, A.F., The geometry of discrete groups, Springer-Verlag, New York, 1983.
  • [4] Carathéodory, C., The most general transformations of plane regions which transform circles into circles. Bull. Am. Math. Soc. 43, (1937), 573–579.
  • [5] Demirel, O. and Seyrantepe, E.S., A characterization of Möbius transformations by use of hyperbolic regular polygons. J. Math. Anal. Appl. 374 (2011), no. 2, 566–572.
  • [6] Demirel, O., A characterization of Möbius transformations by use of hyperbolic regular star polygons. Proc. Rom. Acad. Ser. A Math. Phys. Tech. Sci. Inf. Sci. 14 (2013), no. 1, 13–19.
  • [7] Demirel, O., Degenerate Lambert quadrilaterals and Möbius transformations. Bull. Math. Soc. Sci. Math. Roumanie, (accepted for publication).
  • [8] Haruki, H and Rassias, T.M., A new characteristic of Möbius transformations by use of Apollonius quadrilaterals. Proc. Amer. Math. Soc. 126 (1998), no. 10, 2857–2861.
  • [9] Höfer, R., A characterization of Möbius transformations. Proc. Amer. Math. Soc. 128 (2000), no. 4, 1197–1201.
  • [10] Jing, L., A new characteristic of Möbius transformations by use of polygons having type A. J. Math. Anal. Appl. 324 (2006), no. 1, 281–284.
  • [11] Jones, G.A and Singerman, D., Complex functions. An algebraic and geometric viewpoint. Cambridge University Press, Cambridge, 1987.
  • [12] Ungar, A.A., Analytic hyperbolic geometry. Mathematical foundations and applications. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005
  • [13] Ungar, A.A., The hyperbolic square and Möbius transformations, Banach J. Math. Anal. 1 (2007), no. 1, 101–116.
  • [14] Yang, S. and Fang, A., A new characteristic of Möbius transformations in hyperbolic geometry. J. Math. Anal. Appl. 319 (2006), no. 2, 660–664.
  • [15] Yang, S. and Fang, A., Corrigendum to "A new characteristic of Möbius transformations in hyperbolic geometry, J. Math. Anal. Appl. 319 (2) (2006) 660-664" J. Math. Anal. Appl. 376 (2011), no. 1, 383–384.
Yıl 2017, Cilt: 10 Sayı: 2, 32 - 36, 29.10.2017
https://doi.org/10.36890/iejg.545044

Öz

Kaynakça

  • [1] Aczél, J. and McKiernan, M.A., On the characterization of plane projective and complex Möbius transformations. Math. Nachr. 33, (1967), 315–337.
  • [2] Beardon, A.F. and Minda, D., Sphere-preserving maps in inversive geometry. Proc. Amer. Math. Soc. 130 (2002), no. 4, 987–998.
  • [3] Beardon, A.F., The geometry of discrete groups, Springer-Verlag, New York, 1983.
  • [4] Carathéodory, C., The most general transformations of plane regions which transform circles into circles. Bull. Am. Math. Soc. 43, (1937), 573–579.
  • [5] Demirel, O. and Seyrantepe, E.S., A characterization of Möbius transformations by use of hyperbolic regular polygons. J. Math. Anal. Appl. 374 (2011), no. 2, 566–572.
  • [6] Demirel, O., A characterization of Möbius transformations by use of hyperbolic regular star polygons. Proc. Rom. Acad. Ser. A Math. Phys. Tech. Sci. Inf. Sci. 14 (2013), no. 1, 13–19.
  • [7] Demirel, O., Degenerate Lambert quadrilaterals and Möbius transformations. Bull. Math. Soc. Sci. Math. Roumanie, (accepted for publication).
  • [8] Haruki, H and Rassias, T.M., A new characteristic of Möbius transformations by use of Apollonius quadrilaterals. Proc. Amer. Math. Soc. 126 (1998), no. 10, 2857–2861.
  • [9] Höfer, R., A characterization of Möbius transformations. Proc. Amer. Math. Soc. 128 (2000), no. 4, 1197–1201.
  • [10] Jing, L., A new characteristic of Möbius transformations by use of polygons having type A. J. Math. Anal. Appl. 324 (2006), no. 1, 281–284.
  • [11] Jones, G.A and Singerman, D., Complex functions. An algebraic and geometric viewpoint. Cambridge University Press, Cambridge, 1987.
  • [12] Ungar, A.A., Analytic hyperbolic geometry. Mathematical foundations and applications. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005
  • [13] Ungar, A.A., The hyperbolic square and Möbius transformations, Banach J. Math. Anal. 1 (2007), no. 1, 101–116.
  • [14] Yang, S. and Fang, A., A new characteristic of Möbius transformations in hyperbolic geometry. J. Math. Anal. Appl. 319 (2006), no. 2, 660–664.
  • [15] Yang, S. and Fang, A., Corrigendum to "A new characteristic of Möbius transformations in hyperbolic geometry, J. Math. Anal. Appl. 319 (2) (2006) 660-664" J. Math. Anal. Appl. 376 (2011), no. 1, 383–384.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Oğuzhan Demirel

Yayımlanma Tarihi 29 Ekim 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 10 Sayı: 2

Kaynak Göster

APA Demirel, O. (2017). Degenerate Saccheri Quadrilaterals, Möbius Transformations and Conjugate Möbius Transformations. International Electronic Journal of Geometry, 10(2), 32-36. https://doi.org/10.36890/iejg.545044
AMA Demirel O. Degenerate Saccheri Quadrilaterals, Möbius Transformations and Conjugate Möbius Transformations. Int. Electron. J. Geom. Ekim 2017;10(2):32-36. doi:10.36890/iejg.545044
Chicago Demirel, Oğuzhan. “Degenerate Saccheri Quadrilaterals, Möbius Transformations and Conjugate Möbius Transformations”. International Electronic Journal of Geometry 10, sy. 2 (Ekim 2017): 32-36. https://doi.org/10.36890/iejg.545044.
EndNote Demirel O (01 Ekim 2017) Degenerate Saccheri Quadrilaterals, Möbius Transformations and Conjugate Möbius Transformations. International Electronic Journal of Geometry 10 2 32–36.
IEEE O. Demirel, “Degenerate Saccheri Quadrilaterals, Möbius Transformations and Conjugate Möbius Transformations”, Int. Electron. J. Geom., c. 10, sy. 2, ss. 32–36, 2017, doi: 10.36890/iejg.545044.
ISNAD Demirel, Oğuzhan. “Degenerate Saccheri Quadrilaterals, Möbius Transformations and Conjugate Möbius Transformations”. International Electronic Journal of Geometry 10/2 (Ekim 2017), 32-36. https://doi.org/10.36890/iejg.545044.
JAMA Demirel O. Degenerate Saccheri Quadrilaterals, Möbius Transformations and Conjugate Möbius Transformations. Int. Electron. J. Geom. 2017;10:32–36.
MLA Demirel, Oğuzhan. “Degenerate Saccheri Quadrilaterals, Möbius Transformations and Conjugate Möbius Transformations”. International Electronic Journal of Geometry, c. 10, sy. 2, 2017, ss. 32-36, doi:10.36890/iejg.545044.
Vancouver Demirel O. Degenerate Saccheri Quadrilaterals, Möbius Transformations and Conjugate Möbius Transformations. Int. Electron. J. Geom. 2017;10(2):32-6.