Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2017, , 423 - 431, 30.06.2017
https://doi.org/10.18466/cbayarfbe.319911

Öz

Kaynakça

  • [1] Bruce, J.W.; Giblin, P.J. Curves and Singularities, second edition, Cambridge Univ.Press, 1992.
  • [2] Giering, O. Vorlesungen Über Höhere Geometrie, Fri-edr. Vieweg & Sohn, Braunschweig, Germany, 1982. [3] Arnol'd, V.I.; Gusein-Zade, S.M.; Varchenko, A.N. Singu-larities of Differentiable Maps vol. I, Birkhäuser, 1986.
  • [4] Mond, D. Singularities of the tangent developable surfa-ce of aspace curve, Quart. J. Math. Oxford, 1989; 40, 79-91.
  • [5] Sahin, T.; Yılmaz, M. On singularities of the Galilean spherical darboux ruled surface of a space curve in , Ukranian Math. Journal, 2011; 62(10), 1597-1610. [6] Sahin, T.; Yılmaz, M. The rectifying developable and the tangent indicatrix of a curve in Galilean 3-space, Acta Math. Hungar. 2011; 132(1-2), 154-167.
  • [7] Izumiya, S.; Katsumi, H.; Yamasaki, T. The Rectifying developable and the spherical darboux image of a space curve, Geometry and topology of caustics '98 -- Banach Center Publications. 1999; 50, 137-149.
  • [8] Che, M.G.; Jiang, Y.; Pei, D. The hyperbolic Darboux image and rektifying Gaussian surface of nonlightlike curve in Minkowski 3-space, Journal of Math. Research & Exposition. 2008; 28, 651-658.
  • [9] Molnar, E. The projective interpretation of the eight 3-dimensional homogeneous geometries, Beitr. Algebra Geom. 1997; 38, 261-288.
  • [10] Erjavec, Z.; Divjak, B. The general solution of the Fre-net system of differential equations for curves in the pseu-do-Galilean space , Mathematical Communications. 1997; 2, 143-147. [11] Divjak, B. Geometrija psudogalilejevih prostora, Ph.D. Thesis, University of Zagreb. 1997.
  • [12] Divjak, B.; Šipuš, Ž.M. Special curves on ruled surfaces in Galilean and pseudo-Galilean spaces, Acta Math. Hun-gar., 2003; 98(3), 203-215.
  • [13] Yaglom, I.M. A Simple Non-Euclidean Geometry and Physical Basis, Springer-Verlag Newyork. 1979.

Singularities of the Darboux ruled surface of a space curve in the pseudo-Galilean space

Yıl 2017, , 423 - 431, 30.06.2017
https://doi.org/10.18466/cbayarfbe.319911

Öz


In this article, we establish the singularity theory
in a pseudo-Galilean space
,
a special case of Cayley-Klein spaces. We consider the cases where the Darboux
ruled surface in
 is diffeomorphic to some surfaces in the
neighbourhood of a singular point.  In
addition, we investigate the relationship between singularities of
discriminant, bifurcation sets of the function, and geometric invariants of
curves in
.
 





Kaynakça

  • [1] Bruce, J.W.; Giblin, P.J. Curves and Singularities, second edition, Cambridge Univ.Press, 1992.
  • [2] Giering, O. Vorlesungen Über Höhere Geometrie, Fri-edr. Vieweg & Sohn, Braunschweig, Germany, 1982. [3] Arnol'd, V.I.; Gusein-Zade, S.M.; Varchenko, A.N. Singu-larities of Differentiable Maps vol. I, Birkhäuser, 1986.
  • [4] Mond, D. Singularities of the tangent developable surfa-ce of aspace curve, Quart. J. Math. Oxford, 1989; 40, 79-91.
  • [5] Sahin, T.; Yılmaz, M. On singularities of the Galilean spherical darboux ruled surface of a space curve in , Ukranian Math. Journal, 2011; 62(10), 1597-1610. [6] Sahin, T.; Yılmaz, M. The rectifying developable and the tangent indicatrix of a curve in Galilean 3-space, Acta Math. Hungar. 2011; 132(1-2), 154-167.
  • [7] Izumiya, S.; Katsumi, H.; Yamasaki, T. The Rectifying developable and the spherical darboux image of a space curve, Geometry and topology of caustics '98 -- Banach Center Publications. 1999; 50, 137-149.
  • [8] Che, M.G.; Jiang, Y.; Pei, D. The hyperbolic Darboux image and rektifying Gaussian surface of nonlightlike curve in Minkowski 3-space, Journal of Math. Research & Exposition. 2008; 28, 651-658.
  • [9] Molnar, E. The projective interpretation of the eight 3-dimensional homogeneous geometries, Beitr. Algebra Geom. 1997; 38, 261-288.
  • [10] Erjavec, Z.; Divjak, B. The general solution of the Fre-net system of differential equations for curves in the pseu-do-Galilean space , Mathematical Communications. 1997; 2, 143-147. [11] Divjak, B. Geometrija psudogalilejevih prostora, Ph.D. Thesis, University of Zagreb. 1997.
  • [12] Divjak, B.; Šipuš, Ž.M. Special curves on ruled surfaces in Galilean and pseudo-Galilean spaces, Acta Math. Hun-gar., 2003; 98(3), 203-215.
  • [13] Yaglom, I.M. A Simple Non-Euclidean Geometry and Physical Basis, Springer-Verlag Newyork. 1979.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Makaleler
Yazarlar

Tevfik Şahin Bu kişi benim

Yayımlanma Tarihi 30 Haziran 2017
Yayımlandığı Sayı Yıl 2017

Kaynak Göster

APA Şahin, T. (2017). Singularities of the Darboux ruled surface of a space curve in the pseudo-Galilean space. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, 13(2), 423-431. https://doi.org/10.18466/cbayarfbe.319911
AMA Şahin T. Singularities of the Darboux ruled surface of a space curve in the pseudo-Galilean space. CBUJOS. Haziran 2017;13(2):423-431. doi:10.18466/cbayarfbe.319911
Chicago Şahin, Tevfik. “Singularities of the Darboux Ruled Surface of a Space Curve in the Pseudo-Galilean Space”. Celal Bayar Üniversitesi Fen Bilimleri Dergisi 13, sy. 2 (Haziran 2017): 423-31. https://doi.org/10.18466/cbayarfbe.319911.
EndNote Şahin T (01 Haziran 2017) Singularities of the Darboux ruled surface of a space curve in the pseudo-Galilean space. Celal Bayar Üniversitesi Fen Bilimleri Dergisi 13 2 423–431.
IEEE T. Şahin, “Singularities of the Darboux ruled surface of a space curve in the pseudo-Galilean space”, CBUJOS, c. 13, sy. 2, ss. 423–431, 2017, doi: 10.18466/cbayarfbe.319911.
ISNAD Şahin, Tevfik. “Singularities of the Darboux Ruled Surface of a Space Curve in the Pseudo-Galilean Space”. Celal Bayar Üniversitesi Fen Bilimleri Dergisi 13/2 (Haziran 2017), 423-431. https://doi.org/10.18466/cbayarfbe.319911.
JAMA Şahin T. Singularities of the Darboux ruled surface of a space curve in the pseudo-Galilean space. CBUJOS. 2017;13:423–431.
MLA Şahin, Tevfik. “Singularities of the Darboux Ruled Surface of a Space Curve in the Pseudo-Galilean Space”. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, c. 13, sy. 2, 2017, ss. 423-31, doi:10.18466/cbayarfbe.319911.
Vancouver Şahin T. Singularities of the Darboux ruled surface of a space curve in the pseudo-Galilean space. CBUJOS. 2017;13(2):423-31.