Research Article
Year 2019,
, 135 - 143, 27.03.2019
Abstract
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.
Year 2019,
, 135 - 143, 27.03.2019
Abstract
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.
There are 20 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Publication Date | March 27, 2019 |
| Published in Issue | Year 2019 |