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Tubular Surfaces Around a Null Curve and Its Spherical Images

Year 2021, Volume: 4 Issue: 3, 210 - 220, 30.09.2021
https://doi.org/10.33401/fujma.951273

Abstract

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.

References

  • [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.
Year 2021, Volume: 4 Issue: 3, 210 - 220, 30.09.2021
https://doi.org/10.33401/fujma.951273

Abstract

References

  • [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.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Fatma Ates 0000-0002-3529-1077

Publication Date September 30, 2021
Submission Date June 11, 2021
Acceptance Date September 14, 2021
Published in Issue Year 2021 Volume: 4 Issue: 3

Cite

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. September 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, no. 3 (September 2021): 210-20. https://doi.org/10.33401/fujma.951273.
EndNote Ates F (September 1, 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, vol. 4, no. 3, pp. 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 (September 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, vol. 4, no. 3, 2021, pp. 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.

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