An Application of Ritt-Wu's Zero Decomposition Algorithm to Null Bertrand Type Curves in Minkowski 3-Space  ABSTRACT  |  FULL TEXT 

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References

1. Balgetir, H., Bekta¸s, M. and Inoguchi, J. Null Bertrand curves in Minkowski 3-space and their characterizations, Note Mat. 23 (1), 7–13, 2004/05.
2. Bertrand, J. M. M´emoire sur la th´eorie des courbes ´a double courbure, Comptes Rendus 36, 1850.
3. C¸ ¨oken, C. and C¸ iftci, ¨U. On the Cartan curvatures of a null curve in Minkowski spacetime, Geometriae Dedicata 114, 71–78, 2005.
4. Duggal, K. L. A report on canonical null curves and screen distributions for lightlike geom- etry, Acta Appl. Math. 95, 135–149, 2007.
5. Duggal, K. L. and Bejancu, A. Lightlike Submanifolds of Semi-Riemannian Manifolds and applications(Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht, 1996).
6. Ferr´ndez, A., Gim´nez A. and Lucas, P. Characterization of null curves in Lorentz- andez, A., Gim´enez A. and Lucas, P. Characterization of null curves in Lorentz- Minkowski spaces, Proceedings of the IX Fall Workshop on Geometry and Physics, Vilanova i la Geltru, Publicaciones de la RSME 3, 221–226, 2000.
7. Honda, K. and Inoguchi, J. Deformations of Cartan framed null curves preserving the torsion, Differ. Geom. Dyn. Syst. 5 (1), 31–37, 2003.
8. Inoguchi, J. and Lee, S. Null curves in Minkowski 3-space, Int. Electron. J. Geom. 1 (2), 40–83, 2008.

9. ˙Ilarslan, K. and Yıldırım, M. An Application of Ritt-Wu’s zero decomposition algorithm to the pseudo null Bertrand type curves in Minkowski 3-space, J. Syst. Sci. Complex, To appear, 2009.
10. Kuhnel, W. Differential geometry: curves-surfaces-manifolds (Braunschweig, Wiesbaden, 1999).
11. Liu, H. and Wang, F. Mannheim partner curves in 3-space, Journal of Geometry 88, 120– 126, 2008.
12. O’Neill, B. Semi-Riemannian geometry with applications to relativity (Academic Press, New York, 1983).
13. Ritt, J. F. Differential Algebra (New York, Amer. Math. Soc. Colloquium, 1950).
14. Chou Shang-Ching and Gao Xiao-shan, Automated reasoning in differential geometry and mechanics: Part 1. An improved version of Ritt-Wu’s decomposition algorithm, J. of Au- tomated Reasoning 10, 161–172, 1993.
15. Chou, Shang-Ching and Gao Xiao-shan, Automated reasoning in differential geometry and mechanics: Part 2: Mechanical theorem proving, J. of Automated Reasoning 10, 173–189, 1993.
16. Chou, Shang-Ching and Gao Xiao-shan, Automated reasoning in differential geometry and mechanics: Part 3: Mechanical formula derivation, IFIP Transaction on automated rea- soning, 1–12, 1993.
17. Chou Shang-Ching and Gao Xiao-shan, Automated reasoning in differential geometry and mechanics: Part 4: Bertrand curves, System Sciences and Mathematical Sciences 6 (2), 186–192, 1993.
18. Saint Venant, B. M´emoire sur les lignes courbes non planes, Journal de l’Ecole Polytechnique 18, 1–76, 1845.
19. Wu, W. -T. On the decision problem and the mechanization of theorem-proving in elemen- tary geometry, Scientia Sinica 21, 159–172, 1978.
20. Wu, W. -T. Mechanical derivation of Newton’s gravitational laws from Kepler’s laws, MM- Preprints, MMRC 1, 53–61, 1987.
21. Wu, W. -T. On the foundation of algebraic differential geometry, Systems Sci. Math. Sci. 2, 289–312, 1989.
22. Wu, W. -T. A mechanization method of geometry and its applications II. Curve pairs of Bertrand type, Kexue Tongbao 32, 585–588, 1987.
23. Wu, W. -T. Mechanical theorem proving of differential geometries and some of its applica- tions in mechanics, J. Automat. Reason 7 (2), 171–191, 1991.