Research Article
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Year 2022, Volume: 25 Issue: 3, 1211 - 1215, 01.10.2022
https://doi.org/10.2339/politeknik.870539

Abstract

References

  • [1] O'Neill B., “Semi-Riemannian Geometry with Applications to Relativity”, Academic Press Lim., London, (1983).
  • [2] Willmore T.J., “An Introduction to Differential Geometry”, Oxford University Press, Delhi, (1959).
  • [3] do Carmo M.P., “Differential Geometry of Curves and Surfaces”, Englewood Cliffs, Prentice Hall, (1976).
  • [4] Wang G.J., Tang K. and Tai C.L., “Parametric representation of a surface pencil with a common spatial geodesic”, Comput. Aided Design, 36: 447-459, (2004).
  • [5] Kasap E. and Akyıldız F.T., “Surfaces with common geodesic in Minkowski 3-space”, Appl. Math. Comput., 177: 260-270, (2006).
  • [6] Li C.Y., Wang R.H. and Zhu C.G., “Parametric representation of a surface pencil with a common line of curvature”, Comput. Aided Design, 43: 1110-1117, (2011).
  • [7] Bayram E., Güler F. and Kasap E., “Parametric representation of a surface pencil with a common asymptotic curve”, Comput. Aided Design, 44: 637-643, (2012).
  • [8] Bayram E. and Bilici M., “Surface family with a common involute asymptotic curve”, Int. J. Geom. Methods Modern Phys., 13: 1650062, (2016).
  • [9] Güler F., Bayram E. and Kasap E., “Offset surface pencil with a common asymptotic curve”, Int. J. Geom. Methods Modern Phys., 15: 1850195, (2018).
  • [10] Şaffak Atalay G. and Kasap E., “Surfaces family with common null asymptotic”, Appl. Math. Comput., 260: 135-139, (2015).
  • [11] Yüzbaşı Z.K., “On a family of surfaces with common asymptotic curve in the Galilean space G3”, J. Nonlinear Sci. Appl., 9: 518-523, (2016).
  • [12] Şaffak Atalay G., Bayram E. and Kasap E., “Surface family with a common asymptotic curve in Minkowski 3-space”, Journal of Science and Arts, 2, 43: 357-368, (2018).
  • [13] Yoon D.W., Yüzbaşı Z.K. and Bektaş M., “An approach for surfaces using an asymptotic curve in Lie Group”, Journal of Advanced Physics, 6, 4: 586-590, (2017).
  • [14] Bayram E., “Surface pencil with a common adjoint curve”, Turkish Journal of Mathematics, 44: 1649 – 1659, (2020).
  • [15] Coşanoğlu H., Bayram E., “Surfaces with constant mean curvature along a curve in 3-dimensional Euclidean space”, Süleyman Demirel University, Journal of Natural and Applied Sciences, 24, 3: 533-538, (2020).
  • [16] Walrave J., “Curves and surfaces in Minkowski space”, PhD. Thesis, K. U. Leuven Faculteit Der Wetenschappen, (1995).
  • [17] Lopez R., “Differential geometry of curves and surfaces in Lorentz-Minkowski space”, Int. El. J. of Geometry, 7, 1: 44-107, (2014).

Construction of Surfaces with Constant Mean Curvature Along a Timelike Curve

Year 2022, Volume: 25 Issue: 3, 1211 - 1215, 01.10.2022
https://doi.org/10.2339/politeknik.870539

Abstract

We construct surfaces with constant mean curvature through a given timelike curve. We show that, it is possible to obtain such surfaces for any given timelike curve. The validity of the method supported with illustrative examples.

References

  • [1] O'Neill B., “Semi-Riemannian Geometry with Applications to Relativity”, Academic Press Lim., London, (1983).
  • [2] Willmore T.J., “An Introduction to Differential Geometry”, Oxford University Press, Delhi, (1959).
  • [3] do Carmo M.P., “Differential Geometry of Curves and Surfaces”, Englewood Cliffs, Prentice Hall, (1976).
  • [4] Wang G.J., Tang K. and Tai C.L., “Parametric representation of a surface pencil with a common spatial geodesic”, Comput. Aided Design, 36: 447-459, (2004).
  • [5] Kasap E. and Akyıldız F.T., “Surfaces with common geodesic in Minkowski 3-space”, Appl. Math. Comput., 177: 260-270, (2006).
  • [6] Li C.Y., Wang R.H. and Zhu C.G., “Parametric representation of a surface pencil with a common line of curvature”, Comput. Aided Design, 43: 1110-1117, (2011).
  • [7] Bayram E., Güler F. and Kasap E., “Parametric representation of a surface pencil with a common asymptotic curve”, Comput. Aided Design, 44: 637-643, (2012).
  • [8] Bayram E. and Bilici M., “Surface family with a common involute asymptotic curve”, Int. J. Geom. Methods Modern Phys., 13: 1650062, (2016).
  • [9] Güler F., Bayram E. and Kasap E., “Offset surface pencil with a common asymptotic curve”, Int. J. Geom. Methods Modern Phys., 15: 1850195, (2018).
  • [10] Şaffak Atalay G. and Kasap E., “Surfaces family with common null asymptotic”, Appl. Math. Comput., 260: 135-139, (2015).
  • [11] Yüzbaşı Z.K., “On a family of surfaces with common asymptotic curve in the Galilean space G3”, J. Nonlinear Sci. Appl., 9: 518-523, (2016).
  • [12] Şaffak Atalay G., Bayram E. and Kasap E., “Surface family with a common asymptotic curve in Minkowski 3-space”, Journal of Science and Arts, 2, 43: 357-368, (2018).
  • [13] Yoon D.W., Yüzbaşı Z.K. and Bektaş M., “An approach for surfaces using an asymptotic curve in Lie Group”, Journal of Advanced Physics, 6, 4: 586-590, (2017).
  • [14] Bayram E., “Surface pencil with a common adjoint curve”, Turkish Journal of Mathematics, 44: 1649 – 1659, (2020).
  • [15] Coşanoğlu H., Bayram E., “Surfaces with constant mean curvature along a curve in 3-dimensional Euclidean space”, Süleyman Demirel University, Journal of Natural and Applied Sciences, 24, 3: 533-538, (2020).
  • [16] Walrave J., “Curves and surfaces in Minkowski space”, PhD. Thesis, K. U. Leuven Faculteit Der Wetenschappen, (1995).
  • [17] Lopez R., “Differential geometry of curves and surfaces in Lorentz-Minkowski space”, Int. El. J. of Geometry, 7, 1: 44-107, (2014).
There are 17 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Ergin Bayram 0000-0003-2633-0991

Publication Date October 1, 2022
Submission Date January 29, 2021
Published in Issue Year 2022 Volume: 25 Issue: 3

Cite

APA Bayram, E. (2022). Construction of Surfaces with Constant Mean Curvature Along a Timelike Curve. Politeknik Dergisi, 25(3), 1211-1215. https://doi.org/10.2339/politeknik.870539
AMA Bayram E. Construction of Surfaces with Constant Mean Curvature Along a Timelike Curve. Politeknik Dergisi. October 2022;25(3):1211-1215. doi:10.2339/politeknik.870539
Chicago Bayram, Ergin. “Construction of Surfaces With Constant Mean Curvature Along a Timelike Curve”. Politeknik Dergisi 25, no. 3 (October 2022): 1211-15. https://doi.org/10.2339/politeknik.870539.
EndNote Bayram E (October 1, 2022) Construction of Surfaces with Constant Mean Curvature Along a Timelike Curve. Politeknik Dergisi 25 3 1211–1215.
IEEE E. Bayram, “Construction of Surfaces with Constant Mean Curvature Along a Timelike Curve”, Politeknik Dergisi, vol. 25, no. 3, pp. 1211–1215, 2022, doi: 10.2339/politeknik.870539.
ISNAD Bayram, Ergin. “Construction of Surfaces With Constant Mean Curvature Along a Timelike Curve”. Politeknik Dergisi 25/3 (October 2022), 1211-1215. https://doi.org/10.2339/politeknik.870539.
JAMA Bayram E. Construction of Surfaces with Constant Mean Curvature Along a Timelike Curve. Politeknik Dergisi. 2022;25:1211–1215.
MLA Bayram, Ergin. “Construction of Surfaces With Constant Mean Curvature Along a Timelike Curve”. Politeknik Dergisi, vol. 25, no. 3, 2022, pp. 1211-5, doi:10.2339/politeknik.870539.
Vancouver Bayram E. Construction of Surfaces with Constant Mean Curvature Along a Timelike Curve. Politeknik Dergisi. 2022;25(3):1211-5.