On Ruled Surfaces with Pseudo Null Base Curve in Minkowski 3-Space

Year 2016, Volume: 9 Issue: 2, 9 - 20, 30.10.2016

Emilija Nešović , Ufuk Öztürk Esra B. Koç Öztürk Kazım İlarslan

https://doi.org/10.36890/iejg.584573

Cited By: 4

Abstract

Keywords

Ruled surface, Pseudo null curve, Minkowski space, Distribution parameter, Striction curve

References

• [1] Abdel-All, N. H., Abdel-Baky, R. A., Hamdoon, F. M. Ruled surfaces with timelike rulings, Applied Mathematics and Computation, 147(2004),no. 1, 241-253.
• [2] Barros, M., Ferrández, A., How big is the family of stationary null scrolls?, Journal of Geometry and Physics, 64(2013), 54–60.
• [3] Chino, S., Izumiya, S., Lightlike developables in Minkowski 3-space, Demonstratio Mathematica , 43(2010), no. 2, 387–399.
• [4] Dillen, F., Kuhnel, W., Ruled Weingarten surfaces in Minkowski 3-space, Manuscripta Mathematica, 98(1999), no. 3, 307–320.
• [5] Erdoğdu, M., Özdemir, M., Geometry of Hasimoto Surfaces in Minkowski 3-Space, Mathematical Physics, Analysis and Geometry, 17(2014), no. 1, 169–181.
• [6] Ferrández, A., Lucas, P., On the Gauss map of B-scrolls in 3-dimensional Lorentzian space forms, Czechoslovak Mathematical Journal,50(125) (2000), no. 4, 699–704.
• [7] Foertsch, T., Hasse, W., Perlick, V., Inertial forces and photon surfaces in arbitrary spacetimes, Classical Quantum Gravity, 20(2003), no. 21, 4635–4651.
• [8] Liu, H., Ruled surfaces with lightlike ruling in Minkowski 3-space. Journal of Geometry and Physics, 59(2009), no. 1, 74–78.
• [9] Liu, H., Characterizations of ruled surfaces with lightlike ruling in Minkowski 3-space, Results in Mathematics, 56(2009), no. 1-4, 357–368.
• [10] O’Neill, B., Semi-Riemannian geometry with applications to relativity, Academic Press, New York, 1983.
• [11] Peternell, M., Pottmann, H., Ravani, B., On the computational geometry of ruled surfaces, Computer-Aided Design, 31(1999), 17–32.
• [12] Pottmann, H., Wallner, J., Approximation algorithms for developable surfaces, Comput Aided Geom Design, 16(1999), 539–556.
• [13] Struik, D. J., Lectures on Classical Differential Geometry, Dover Publications, New York, 1988.
• [14] Turgut, A., Hacısalihoğlu, H. H., Timelike ruled surfaces in the Minkowski 3-space. II, Turkish Journal of Mathematics, 22(1998), no. 1, 33–46.
• [15] Walrave, J., Curves and surfaces in Minkowski space, Ph.D. thesis, Katholieke Universiteit Leuven, Belgium 1995.
• [16] Wang, D. L., Liu, J., Xiao, D. Z., Kinematic differential geometry of a rigid body in spatial motion-II. A new adjoint approach and instantaneous properties of a line trajectory in spatial kinematics, Mechanism and Machine Theory, 32(1997), no. 4, 433-444.
• [17] Yayli, Y., Saracoglu, S., On developable ruled surfaces in Minkowski space, Advances in Applied Clifford Algebras, 22(2012), no. 2, 499–510.