Ergin BAYRAM

Construction of Surfaces with Constant Mean Curvature Along a Timelike Curve

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.

Keywords:

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

PDF

___

[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).