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Rulings on the Surfaces Having Null Axis and Null Profile Curve in Lorentz-Minkowski 3-Space

Year 2022, Volume: 15 Issue: 1, 11 - 19, 30.04.2022
https://doi.org/10.36890/iejg.1064158

Abstract

We define the curves family of the surfaces with null profile curve and null axis, and give some smooth functions in three dimensional Lorentz-Minkowski space $\mathbb{L}^{3}$. In addition, we compute the third Laplace-Beltrami operator of this type surfaces.

References

  • Baikoussis, Chr., Koufogiorgos, T.: Helicoidal surfaces with prescribed mean or a Gaussian curvature. J. Geom. 63, 25–29 (1998).
  • Beneki, Chr. C., Kaimakamis, G., Papantoniou, B.J.: A classification of surfaces of revolution of constant Gaussian curvature in the Minkowski space R3 1. Bull. Calcutta Math. Soc. 90, 441–458 (1998).
  • Beneki, Chr. C., Kaimakamis, G., Papantoniou, B.J.: Helicoidal surfaces in three-dimensional Minkowski space. J. Math. Anal. Appl. 275, 586–614 (2002).
  • Bobenko, A.I.: Constant mean curvature surfaces and integrable equations. Russian Math. Soc. 46, 1–45 (1991).
  • Do Carmo, M.P., Dajczer, M.: Helicoidal surfaces with constant mean curvature. Tohôku Math. J. 34, 425–435 (1982).
  • Choi, S.M.: On the Gauss map of surfaces of revolution in a 3-dimensional Minkowski space. Tsukuba J. Math. 19, 351–366 (1996).
  • Crambin, M., Pirani, F.A.E.: Applicable Differential Geometry. London Math. Soc. Lecture Notes Series, Vol. 59, Cambridge Un. Press, London, (1986).
  • Dillen, F., Kühnel, W.: Ruled Weingarten surfaces in Minkowski 3-space. Manuscripta Math. 98, 307–320 (1999).
  • Eisenhart, L.: A Treastise on the Differential Geometry of Curves and Surfaces. Palermo 41 Ginn and Company, USA (1909).
  • Güler, E.: Bour’s theorem and light-like profile curve. Yokohama Math. J. 54 (1) 55–77 (2007).
  • Güler, E., Vanlı, A.: Bour’s theorem in Minkowski 3-space. J. Math. Kyoto. 46 (1) 47–63 (2006).
  • Güler, E., Yaylı, Y., Hacısaliho˘glu, H.H.: Bour’s theorem on Gauss map in Euclidean 3-space. Hacett. J. Math. Stat., 39 (4), 515–525 (2010).
  • Hano, J., Nomizu, K.: Surfaces of revolution with constant mean curvature in Lorentz-Minkowski space. Tohoku Math. J. 36, 427–437 (1984).
  • Hitt, L., Roussos, I.: Computer graphics of helicoidal surfaces with constant mean curvature. An. Acad. Brasil. Ciênc. 63, 211–228 (1991).
  • Kaimakamis, G., Papantoniou, B., Petoumenos, K.: Surfaces of revolution in the 3-dimensional Lorentz-Minkowski space satisfying ∆III r = Ar. Bull. Greek Math. Soc. 50, 75–90 (2005).
  • Kenmotsu, K.: Surfaces of revolution with prescribed mean curvature. Tohôku Math. J. 32 (1980), 147–153.
  • Sasahara, N.: Spacelike helicoidal surfaces with constant mean curvature in Minkowski 3-space. Tokyo J.Math. 23, 477–502 (2000).
  • Struik, D.J.: Lectures on Differential Geometry. Addison-Wesley, New-York, (1961).
Year 2022, Volume: 15 Issue: 1, 11 - 19, 30.04.2022
https://doi.org/10.36890/iejg.1064158

Abstract

References

  • Baikoussis, Chr., Koufogiorgos, T.: Helicoidal surfaces with prescribed mean or a Gaussian curvature. J. Geom. 63, 25–29 (1998).
  • Beneki, Chr. C., Kaimakamis, G., Papantoniou, B.J.: A classification of surfaces of revolution of constant Gaussian curvature in the Minkowski space R3 1. Bull. Calcutta Math. Soc. 90, 441–458 (1998).
  • Beneki, Chr. C., Kaimakamis, G., Papantoniou, B.J.: Helicoidal surfaces in three-dimensional Minkowski space. J. Math. Anal. Appl. 275, 586–614 (2002).
  • Bobenko, A.I.: Constant mean curvature surfaces and integrable equations. Russian Math. Soc. 46, 1–45 (1991).
  • Do Carmo, M.P., Dajczer, M.: Helicoidal surfaces with constant mean curvature. Tohôku Math. J. 34, 425–435 (1982).
  • Choi, S.M.: On the Gauss map of surfaces of revolution in a 3-dimensional Minkowski space. Tsukuba J. Math. 19, 351–366 (1996).
  • Crambin, M., Pirani, F.A.E.: Applicable Differential Geometry. London Math. Soc. Lecture Notes Series, Vol. 59, Cambridge Un. Press, London, (1986).
  • Dillen, F., Kühnel, W.: Ruled Weingarten surfaces in Minkowski 3-space. Manuscripta Math. 98, 307–320 (1999).
  • Eisenhart, L.: A Treastise on the Differential Geometry of Curves and Surfaces. Palermo 41 Ginn and Company, USA (1909).
  • Güler, E.: Bour’s theorem and light-like profile curve. Yokohama Math. J. 54 (1) 55–77 (2007).
  • Güler, E., Vanlı, A.: Bour’s theorem in Minkowski 3-space. J. Math. Kyoto. 46 (1) 47–63 (2006).
  • Güler, E., Yaylı, Y., Hacısaliho˘glu, H.H.: Bour’s theorem on Gauss map in Euclidean 3-space. Hacett. J. Math. Stat., 39 (4), 515–525 (2010).
  • Hano, J., Nomizu, K.: Surfaces of revolution with constant mean curvature in Lorentz-Minkowski space. Tohoku Math. J. 36, 427–437 (1984).
  • Hitt, L., Roussos, I.: Computer graphics of helicoidal surfaces with constant mean curvature. An. Acad. Brasil. Ciênc. 63, 211–228 (1991).
  • Kaimakamis, G., Papantoniou, B., Petoumenos, K.: Surfaces of revolution in the 3-dimensional Lorentz-Minkowski space satisfying ∆III r = Ar. Bull. Greek Math. Soc. 50, 75–90 (2005).
  • Kenmotsu, K.: Surfaces of revolution with prescribed mean curvature. Tohôku Math. J. 32 (1980), 147–153.
  • Sasahara, N.: Spacelike helicoidal surfaces with constant mean curvature in Minkowski 3-space. Tokyo J.Math. 23, 477–502 (2000).
  • Struik, D.J.: Lectures on Differential Geometry. Addison-Wesley, New-York, (1961).
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Erhan Güler 0000-0003-3264-6239

Early Pub Date April 30, 2022
Publication Date April 30, 2022
Acceptance Date March 9, 2022
Published in Issue Year 2022 Volume: 15 Issue: 1

Cite

APA Güler, E. (2022). Rulings on the Surfaces Having Null Axis and Null Profile Curve in Lorentz-Minkowski 3-Space. International Electronic Journal of Geometry, 15(1), 11-19. https://doi.org/10.36890/iejg.1064158
AMA Güler E. Rulings on the Surfaces Having Null Axis and Null Profile Curve in Lorentz-Minkowski 3-Space. Int. Electron. J. Geom. April 2022;15(1):11-19. doi:10.36890/iejg.1064158
Chicago Güler, Erhan. “Rulings on the Surfaces Having Null Axis and Null Profile Curve in Lorentz-Minkowski 3-Space”. International Electronic Journal of Geometry 15, no. 1 (April 2022): 11-19. https://doi.org/10.36890/iejg.1064158.
EndNote Güler E (April 1, 2022) Rulings on the Surfaces Having Null Axis and Null Profile Curve in Lorentz-Minkowski 3-Space. International Electronic Journal of Geometry 15 1 11–19.
IEEE E. Güler, “Rulings on the Surfaces Having Null Axis and Null Profile Curve in Lorentz-Minkowski 3-Space”, Int. Electron. J. Geom., vol. 15, no. 1, pp. 11–19, 2022, doi: 10.36890/iejg.1064158.
ISNAD Güler, Erhan. “Rulings on the Surfaces Having Null Axis and Null Profile Curve in Lorentz-Minkowski 3-Space”. International Electronic Journal of Geometry 15/1 (April 2022), 11-19. https://doi.org/10.36890/iejg.1064158.
JAMA Güler E. Rulings on the Surfaces Having Null Axis and Null Profile Curve in Lorentz-Minkowski 3-Space. Int. Electron. J. Geom. 2022;15:11–19.
MLA Güler, Erhan. “Rulings on the Surfaces Having Null Axis and Null Profile Curve in Lorentz-Minkowski 3-Space”. International Electronic Journal of Geometry, vol. 15, no. 1, 2022, pp. 11-19, doi:10.36890/iejg.1064158.
Vancouver Güler E. Rulings on the Surfaces Having Null Axis and Null Profile Curve in Lorentz-Minkowski 3-Space. Int. Electron. J. Geom. 2022;15(1):11-9.