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

Kaynakça (19)

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 hyperbol