Construction of Surfaces with Constant Mean Curvature Along a Timelike Curve

Yıl 2022, Cilt: 25 Sayı: 3, 1211 - 1215, 01.10.2022

Ergin Bayram

https://doi.org/10.2339/politeknik.870539

Cited By: 4

Öz

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.

Anahtar Kelimeler

Timelike curve, constant mean curvature surfaces, Minkowski 3-space

Kaynakça

• [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).