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Tubular Surfaces Around a Null Curve and Its Spherical Images

Yıl 2021, Cilt: 4 Sayı: 3, 210 - 220, 30.09.2021

Fatma Ates

https://doi.org/10.33401/fujma.951273
Cited By: 1

Öz

In this study, we define tubular surfaces whose center curves are null curves and their spherical images in Minkowski 3􀀀space. Firstly, we give the interior properties of the surfaces and calculate their invariant curvatures. Then, we obtain some special characterizations for the parameter curves of the surfaces. Finally, we demonstrate the theory via example and give their visualizations with the help of Mathematica.

Anahtar Kelimeler

Asymptotic curve Geodesic curve Images Singular points Tubular surface

Kaynakça

  • [1] E. Cartan, La Theorie Des Groupes Finis et Continus et la Geometrie Differentielle, Gauthier-Villars, Paris, 1937.
  • [2] A. Bejancu, Lightlike curves in Lorentz manifolds, Publ. Math. Debrecen, 44(1) (1994), 145–155.
  • [3] F. Gökçelik, I. G¨ok, NullW􀀀slant helices in E3 1 , J. Math. Anal. Appl., 420 (2014), 222–241.
  • [4] M. K. Karacan, Y. Yaylı, On the geodesics of tubular surfaces in Minkowski 3􀀀space, Bull. Malays. Math. Sci. Soc., 31(2) (2008), 1-10.
  • [5] F. Ates¸, E. Kocakus¸aklı, ˙I. G¨ok, N. Ekmekci, Tubular surfaces formed by semi-spherical indicatrices in E3 1 , Mediterr. J. Math., 17 (127) (2020). https://doi.org/10.1007/s00009-020-01561-z
  • [6] F. Doğan, Y.Yaylı, On the curvatures of Tubular surface with Bishop frame, Commun. Fac. Sci. Univ. Ank. Ser. A1, 60(1) (2011), 59–69
  • [7] F. Doğan, Y. Yaylı, Tubes with Darboux frame, Int. J. Contemp. Math. Sci., 7(16) (2012), 751 - 758.
  • [8] F. Doğan, Generalized canal surfaces, Ph.D. Thesis, Ankara University, 2012.
  • [9] M. K. Karacan, Y. Tunçer, Tubular surfaces of Weingarten types in Galilean and pseudo-Galilean, Bull. Math. Anal. Appl., 5(2) (2013), 87-100.
  • [10] J. Qian J, M. Su, X. Fu, S. D. Jung, Geometric characterizations of canal surfaces in Minkowski 3-space II, Mathematics, 7(8) (2019), 703. https://doi.org/10.3390/math7080703
  • [11] P. A. Blaga, On tubular surfaces in computer graphics, Stud. Univ. Babes¸-Bolyai Inform., 50(2) (2005), 81-90.
  • [12] B. Yildiz, K. Arslan, H. Yildiz, C. O¨ zgu¨r, A geometric description of the ascending colon of some domestic animals, Ann Anat., 183 (2001), 555-557.
  • [13] M. Peternell, H. Potmann, Computing rational parametrizations of canal surfaces, J. Symb. Comput., 23 (1997), 255-266.
  • [14] R. Lopez, Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int. Electron. J. Geom., 7(1) (2014), 44-107.
  • [15] K. L. Duggal, D. H. Jin, Null curves and hypersurfaces of semi-Riemannian manifolds, World Scientific, 2007.
  • [16] R. Lopez, Rotational linear Weingarten surfaces of hyperbolic type. Isr. J. Math., 167 (2008), 283–302.
  • [17] P. Tekin, F. N. Ekmekci, On Weingarten tube surfaces with null curve in Minkowski 3-space, New Trends in Math. Sci., 3(3) (2015), 168-174.
  • [18] H. Liu, Curves in the lightlike cone, Beitr. Algebra Geom., 45(1) (2004), 291-303.

Yıl 2021, Cilt: 4 Sayı: 3, 210 - 220, 30.09.2021

Fatma Ates

https://doi.org/10.33401/fujma.951273
Cited By: 1

Öz

Kaynakça

  • [1] E. Cartan, La Theorie Des Groupes Finis et Continus et la Geometrie Differentielle, Gauthier-Villars, Paris, 1937.
  • [2] A. Bejancu, Lightlike curves in Lorentz manifolds, Publ. Math. Debrecen, 44(1) (1994), 145–155.
  • [3] F. Gökçelik, I. G¨ok, NullW􀀀slant helices in E3 1 , J. Math. Anal. Appl., 420 (2014), 222–241.
  • [4] M. K. Karacan, Y. Yaylı, On the geodesics of tubular surfaces in Minkowski 3􀀀space, Bull. Malays. Math. Sci. Soc., 31(2) (2008), 1-10.
  • [5] F. Ates¸, E. Kocakus¸aklı, ˙I. G¨ok, N. Ekmekci, Tubular surfaces formed by semi-spherical indicatrices in E3 1 , Mediterr. J. Math., 17 (127) (2020). https://doi.org/10.1007/s00009-020-01561-z
  • [6] F. Doğan, Y.Yaylı, On the curvatures of Tubular surface with Bishop frame, Commun. Fac. Sci. Univ. Ank. Ser. A1, 60(1) (2011), 59–69
  • [7] F. Doğan, Y. Yaylı, Tubes with Darboux frame, Int. J. Contemp. Math. Sci., 7(16) (2012), 751 - 758.
  • [8] F. Doğan, Generalized canal surfaces, Ph.D. Thesis, Ankara University, 2012.
  • [9] M. K. Karacan, Y. Tunçer, Tubular surfaces of Weingarten types in Galilean and pseudo-Galilean, Bull. Math. Anal. Appl., 5(2) (2013), 87-100.
  • [10] J. Qian J, M. Su, X. Fu, S. D. Jung, Geometric characterizations of canal surfaces in Minkowski 3-space II, Mathematics, 7(8) (2019), 703. https://doi.org/10.3390/math7080703
  • [11] P. A. Blaga, On tubular surfaces in computer graphics, Stud. Univ. Babes¸-Bolyai Inform., 50(2) (2005), 81-90.
  • [12] B. Yildiz, K. Arslan, H. Yildiz, C. O¨ zgu¨r, A geometric description of the ascending colon of some domestic animals, Ann Anat., 183 (2001), 555-557.
  • [13] M. Peternell, H. Potmann, Computing rational parametrizations of canal surfaces, J. Symb. Comput., 23 (1997), 255-266.
  • [14] R. Lopez, Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int. Electron. J. Geom., 7(1) (2014), 44-107.
  • [15] K. L. Duggal, D. H. Jin, Null curves and hypersurfaces of semi-Riemannian manifolds, World Scientific, 2007.
  • [16] R. Lopez, Rotational linear Weingarten surfaces of hyperbolic type. Isr. J. Math., 167 (2008), 283–302.
  • [17] P. Tekin, F. N. Ekmekci, On Weingarten tube surfaces with null curve in Minkowski 3-space, New Trends in Math. Sci., 3(3) (2015), 168-174.
  • [18] H. Liu, Curves in the lightlike cone, Beitr. Algebra Geom., 45(1) (2004), 291-303.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Fatma Ates 0000-0002-3529-1077

Yayımlanma Tarihi 30 Eylül 2021
Gönderilme Tarihi 11 Haziran 2021
Kabul Tarihi 14 Eylül 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 4 Sayı: 3

Kaynak Göster

APA Ates, F. (2021). Tubular Surfaces Around a Null Curve and Its Spherical Images. Fundamental Journal of Mathematics and Applications, 4(3), 210-220. https://doi.org/10.33401/fujma.951273
AMA Ates F. Tubular Surfaces Around a Null Curve and Its Spherical Images. FUJMA. Eylül 2021;4(3):210-220. doi:10.33401/fujma.951273
Chicago Ates, Fatma. “Tubular Surfaces Around a Null Curve and Its Spherical Images”. Fundamental Journal of Mathematics and Applications 4, sy. 3 (Eylül 2021): 210-20. https://doi.org/10.33401/fujma.951273.
EndNote Ates F (01 Eylül 2021) Tubular Surfaces Around a Null Curve and Its Spherical Images. Fundamental Journal of Mathematics and Applications 4 3 210–220.
IEEE F. Ates, “Tubular Surfaces Around a Null Curve and Its Spherical Images”, FUJMA, c. 4, sy. 3, ss. 210–220, 2021, doi: 10.33401/fujma.951273.
ISNAD Ates, Fatma. “Tubular Surfaces Around a Null Curve and Its Spherical Images”. Fundamental Journal of Mathematics and Applications 4/3 (Eylül 2021), 210-220. https://doi.org/10.33401/fujma.951273.
JAMA Ates F. Tubular Surfaces Around a Null Curve and Its Spherical Images. FUJMA. 2021;4:210–220.
MLA Ates, Fatma. “Tubular Surfaces Around a Null Curve and Its Spherical Images”. Fundamental Journal of Mathematics and Applications, c. 4, sy. 3, 2021, ss. 210-2, doi:10.33401/fujma.951273.
Vancouver Ates F. Tubular Surfaces Around a Null Curve and Its Spherical Images. FUJMA. 2021;4(3):210-2.

Cited By

Canal Surfaces Through a Null Quaternionic Spine Curve
Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi
https://doi.org/10.35193/bseufbd.1059044
 Kapak Resmi İndir

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