In this study, we define tubular surfaces whose center curves are null curves and their spherical images in Minkowski 3space. 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.
[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, NullWslant 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 3space, 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.
[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, NullWslant 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 3space, 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.
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. Fundam. J. Math. Appl. 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”, Fundam. J. Math. Appl., 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. Fundam. J. Math. Appl. 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. Fundam. J. Math. Appl. 2021;4(3):210-2.