On a Spacelike Line Congruence Which Has the Parameter Ruled Surfaces as Principal Ruled Surfaces

Year 2019, Volume: 12 Issue: 1, 135 - 143, 27.03.2019

Ferhat Taş Rashad A. Abdel-baky

https://doi.org/10.36890/iejg.545870

Cited By: 5

Abstract

Keywords

Spacelike line congruence, Hamilton and Mannhiem formulae, Plücker conoid

References

• [1] Abdel-Baky, R.A.; The relation among Darboux vectors of ruled surfaces in a line congruence, Riv. Mat., Univ. Parama, (1997), (5)6, pp.201- 211.
• [2] Abdel-Baky, R.A. On the congruences of the tangents to a surface, Anz. Osterreich. Akad. Wiss. Math.-Natur. Kl., (1999), 136: 9–18.
• [3] Abdel-Baky, R.A. . On instantaneous rectilinear congruences, J. Geom. Graph., (2003), 7(2): 129–135.
• [4] Abdel-Baky, R. A. On a line congruence which has the parameter ruled surfaces as principal ruled surfaces, Applied mathematics and computation, 151.3 (2004): 849-862.
• [5] Blaschke, W.; Vorlesungen uber Differential Geometrie, Bd 1, Dover Publications, New York, pp.260-277, 1945.
• [6] Bottema, O. and Roth, B. Theoretical Kinematics, North-Holland Press, New York, 1979.
• [7] Odehnal, B. and Pottmann, H. Computing with discrete models of ruled surfaces and line congruences, Proceedings of the 2nd workshop on computational kinematics, Seoul 2001.
• [8] Odehnal, B. Geometric Optimization Methods for Line Congruences, Ph. D. Thesis, Vienna University of Technology, 2002.
• [9] O’Neil, B. Semi-Riemannian Geometry with Applications to Relativity. Academic Press, London, 1983.
• [10] Papadopoulou, D. and Koltsaki, P. Triply orthogonal line congruences with common middle surface, J. Geom. Graph., (2010), 14(1): 45–58.
• [11] Pottman, H. and Wallner, J. Computational Line Geometry, Springer-Verlag, Berlin, Heidelberg, 2001.
• [12] F. Ta¸s, 2016, "On the Computational Line Geometry," Ph.D. thesis, Institute of Graduate Studies in Science and Engineering, Istanbul University, Istanbul.
• [13] F. Taş, O. Gürsoy, 2018, On the Line Congruences, International Electronic Journal of Geometry, Vol. 11(2), pp. 47-53.
• [14] Tsagas, Gr. "On the rectilinear congruences of Lorentz manifold establishing an area preserving representation." Tensor, NS 47 (1988): 127-139.
• [15] Tunahan, T., Nurai, Y. and Nihat, A. On pseudohyperbolic space motions, Turk J Math., (2015), 39: 750-762, TUBITAK doi:10.3906/mat- 1503-37.
• [16] Uğurlu, H.H.; Çalışkan, A. The Study Mapping for Directed Space-Like and Time-Like in Minkowski 3-Space R13. Math. Comput. Appl., (1996), 1, 142-148.
• [17] Veldkamp, G.R.; On the use of dual numbers, vectors, and matrices in instantaneous spatial kinematics, Mech. and Mach. Theory, (1976), V.11, pp.141-156.
• [18] Yaglom, I.M. A Simple Non-Euclidean Geometry and Its Physical Basis. Springer-Verlag, New York, 1979.
• [19] Yayli,Y, Caliskan A. and Ugurlu, H.H. The E study maps of circles on dual hyperbolic and Lorentzian unit spheresH20 and S^2_1, Mathematical Proceedings of the Royal Irish Academy, (2002), 102A: 37-47.
• [20] Zhong, H. and Hual, Li, L. A kind of rectilinear congruences in the Minkowski 3-Space, J. of Mathematical Research & Exposition, Nov., 2008, Vol. 28, No. 4 pp. 911–918.