An application of Ritt-Wu’s zero decomposition algorithm to the pseudo null Bertrand type curves in Minkowski 3-space (original) (raw)
Access this article
Subscribe and save
- Starting from 10 chapters or articles per month
- Access and download chapters and articles from more than 300k books and 2,500 journals
- Cancel anytime View plans
Buy Now
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
Instant access to the full article PDF.
References
- B. Saint Venant, Mémoire sur les lignes courbes non planes, Journal de l’Ecole Polytechnique, 1845, 18: 1–76.
Google Scholar - J. M. Bertrand, Mémoire sur la théorie des courbes á double courbure, Comptes Rendus, 1850, 36.
- John F. Burke, Bertrand curves associated with a pair of curves, Mathematics Magazine, 1960, 34(1): 60–62
Article MathSciNet Google Scholar - L. R. Pears, Bertrand curves in Riemannian space, J. London Math. Soc., 1935, s1–10(2): 180–183.
Article Google Scholar - C. Bioche, Sur les courbes de M. Bertrand, Bull. Soc. Math., 1889, 17: 109–112.
MathSciNet Google Scholar - H. Matsuda and S. Yorozu, Notes on Bertrand curves, Yokohama Math. J., 2003, 50(1–2): 41–58.
MATH MathSciNet Google Scholar - H. Balgetir, M. Bektaş, and J. Inoguchi, Null Bertrand curves in Minkowski 3-space and their characterizations, Note Mat., 2004/05, 23(1): 7–13.
MATH MathSciNet Google Scholar - H. Balgetir, M. Bektaş, and M. Ergüt, Bertrand curves for nonnull curves in 3-dimensional Lorentzian space, Hadronic J., 2004, 27(2): 229–236.
MATH MathSciNet Google Scholar - N. Ekmekci and K. İlarslan, On Bertrand curves and their characterization, Differ. Geom. Dyn. Syst., 2001, 3(2): 17–24.
MATH MathSciNet Google Scholar - Wen-Tsun Wu, On the decision problem and the mechanization of theorem-proving in elementary geometry, Scientia Sinica, 1978, 21: 159–172.
MATH MathSciNet Google Scholar - J. F. Ritt, Differential Algebra, Amer. Math. Soc. Colloquium, New York, 1950.
MATH Google Scholar - Wen-Tsun Wu, On the foundation of algebraic differential geometry, Systems Sci. Math. Sci., 1989, 2: 289–312.
MATH MathSciNet Google Scholar - Wen-Tsun Wu, A mechanization method of geometry and its applications II: Curve pairs of Bertrand type, Kexue Tongbao, 1987, 32: 585–588.
MATH Google Scholar - Wen-Tsun Wu, Mechanical derivation of Newton’s gravitational laws from Kepler’s laws, MMPreprints, MMRC, 1987, 1: 53–61.
Google Scholar - S. C. Chou and X. S. Gao, Automated reasoning in differential geometry and mechanics: Part 1: An improved version of Ritt-Wu’s decomposition algorithm, J. of Automated Reasoning, 1993, 10: 161–172.
Article MATH MathSciNet Google Scholar - S. C. Chou and X. S. Gao, Part 2: Mechanical theorem proving, J. of Automated Reasoning, 1993, 10: 173–189.
Article MATH MathSciNet Google Scholar - S. C. Chou and X. S. Gao, Part 3: Mechanical formuladerivation, IFIP Transaction on automated reasoning, 1993: 1–12.
- S. C. Chou and X. S. Gao, Part 4: Bertrand curves, System Sciences and Mathematical Sciences, 1993, 6(2): 186–192.
MATH MathSciNet Google Scholar - B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.
MATH Google Scholar - J. Walrave, Curves and Surfaces in Minkowski Space, Doctoral thesis, K. U. Leuven, Fac. of Science, Leuven, 1995.
Google Scholar - W. B. Bonnor, Curves with Null Normals in Minkowski Space-Time: A Random Walk in Relativity and Cosmology, Wiley Eastern Limited, 1985: 33–47.
- H. Liu and F. Wang, Mannheim partner curves in 3-space, Journal of Geometry, 2008, 88: 120–126.
Article MATH MathSciNet Google Scholar - S. C. Chou and X. S. Gao, Ritt-Wu’s decomposition algorithm and geometry theorem proving, CADE-10, M. E. Stickel (Ed.), Lecture Notes in Comput. Sci., Springer-Verlag, Berlin, 1990, 449: 207–220.
Google Scholar - Wen-Tsun Wu, Mechanical theorem-proving of differential geometries and its applications in mechanics, J. Aut. Reasoning, 1991, 7: 171–191.
MATH Google Scholar