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.
Bertrand, J. M. M´emoire sur la th´eorie des courbes ´a double courbure, Comptes Rendus 36, 1850.
C¸ ¨oken, C. and C¸ iftci, ¨U. On the Cartan curvatures of a null curve in Minkowski spacetime, Geometriae Dedicata 114, 71–78, 2005.
Duggal, K. L. A report on canonical null curves and screen distributions for lightlike geom- etry, Acta Appl. Math. 95, 135–149, 2007.
Duggal, K. L. and Bejancu, A. Lightlike Submanifolds of Semi-Riemannian Manifolds and applications(Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht, 1996).
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.
Honda, K. and Inoguchi, J. Deformations of Cartan framed null curves preserving the torsion, Differ. Geom. Dyn. Syst. 5 (1), 31–37, 2003.
Inoguchi, J. and Lee, S. Null curves in Minkowski 3-space, Int. Electron. J. Geom. 1 (2), 40–83, 2008.
˙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.
Kuhnel, W. Differential geometry: curves-surfaces-manifolds (Braunschweig, Wiesbaden, 1999).
Liu, H. and Wang, F. Mannheim partner curves in 3-space, Journal of Geometry 88, 120– 126, 2008.
O’Neill, B. Semi-Riemannian geometry with applications to relativity (Academic Press, New York, 1983).
Ritt, J. F. Differential Algebra (New York, Amer. Math. Soc. Colloquium, 1950).
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.
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.
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.
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.
Saint Venant, B. M´emoire sur les lignes courbes non planes, Journal de l’Ecole Polytechnique 18, 1–76, 1845.
Wu, W. -T. On the decision problem and the mechanization of theorem-proving in elemen- tary geometry, Scientia Sinica 21, 159–172, 1978.
Wu, W. -T. Mechanical derivation of Newton’s gravitational laws from Kepler’s laws, MM- Preprints, MMRC 1, 53–61, 1987.
Wu, W. -T. On the foundation of algebraic differential geometry, Systems Sci. Math. Sci. 2, 289–312, 1989.
Wu, W. -T. A mechanization method of geometry and its applications II. Curve pairs of Bertrand type, Kexue Tongbao 32, 585–588, 1987.
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.
An Application of Ritt-Wu's Zero Decomposition Algorithm to Null Bertrand Type Curves in Minkowski 3-Space ABSTRACT | FULL TEXT
Year 2010,
Volume: 39 Issue: 4, 555 - 565, 01.04.2010
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.
Bertrand, J. M. M´emoire sur la th´eorie des courbes ´a double courbure, Comptes Rendus 36, 1850.
C¸ ¨oken, C. and C¸ iftci, ¨U. On the Cartan curvatures of a null curve in Minkowski spacetime, Geometriae Dedicata 114, 71–78, 2005.
Duggal, K. L. A report on canonical null curves and screen distributions for lightlike geom- etry, Acta Appl. Math. 95, 135–149, 2007.
Duggal, K. L. and Bejancu, A. Lightlike Submanifolds of Semi-Riemannian Manifolds and applications(Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht, 1996).
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.
Honda, K. and Inoguchi, J. Deformations of Cartan framed null curves preserving the torsion, Differ. Geom. Dyn. Syst. 5 (1), 31–37, 2003.
Inoguchi, J. and Lee, S. Null curves in Minkowski 3-space, Int. Electron. J. Geom. 1 (2), 40–83, 2008.
˙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.
Kuhnel, W. Differential geometry: curves-surfaces-manifolds (Braunschweig, Wiesbaden, 1999).
Liu, H. and Wang, F. Mannheim partner curves in 3-space, Journal of Geometry 88, 120– 126, 2008.
O’Neill, B. Semi-Riemannian geometry with applications to relativity (Academic Press, New York, 1983).
Ritt, J. F. Differential Algebra (New York, Amer. Math. Soc. Colloquium, 1950).
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.
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.
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.
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.
Saint Venant, B. M´emoire sur les lignes courbes non planes, Journal de l’Ecole Polytechnique 18, 1–76, 1845.
Wu, W. -T. On the decision problem and the mechanization of theorem-proving in elemen- tary geometry, Scientia Sinica 21, 159–172, 1978.
Wu, W. -T. Mechanical derivation of Newton’s gravitational laws from Kepler’s laws, MM- Preprints, MMRC 1, 53–61, 1987.
Wu, W. -T. On the foundation of algebraic differential geometry, Systems Sci. Math. Sci. 2, 289–312, 1989.
Wu, W. -T. A mechanization method of geometry and its applications II. Curve pairs of Bertrand type, Kexue Tongbao 32, 585–588, 1987.
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.
Yildirim, M., & Ilarslan, . (2010). An Application of Ritt-Wu’s Zero Decomposition Algorithm to Null Bertrand Type Curves in Minkowski 3-Space ABSTRACT | FULL TEXT . Hacettepe Journal of Mathematics and Statistics, 39(4), 555-565.
AMA
Yildirim M, Ilarslan . An Application of Ritt-Wu’s Zero Decomposition Algorithm to Null Bertrand Type Curves in Minkowski 3-Space ABSTRACT | FULL TEXT . Hacettepe Journal of Mathematics and Statistics. April 2010;39(4):555-565.
Chicago
Yildirim, Mehmet, and kazim Ilarslan. “An Application of Ritt-Wu’s Zero Decomposition Algorithm to Null Bertrand Type Curves in Minkowski 3-Space ABSTRACT | FULL TEXT ”. Hacettepe Journal of Mathematics and Statistics 39, no. 4 (April 2010): 555-65.
EndNote
Yildirim M, Ilarslan (April 1, 2010) An Application of Ritt-Wu’s Zero Decomposition Algorithm to Null Bertrand Type Curves in Minkowski 3-Space ABSTRACT | FULL TEXT . Hacettepe Journal of Mathematics and Statistics 39 4 555–565.
IEEE
M. Yildirim and . Ilarslan, “An Application of Ritt-Wu’s Zero Decomposition Algorithm to Null Bertrand Type Curves in Minkowski 3-Space ABSTRACT | FULL TEXT ”, Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 4, pp. 555–565, 2010.
ISNAD
Yildirim, Mehmet - Ilarslan, kazim. “An Application of Ritt-Wu’s Zero Decomposition Algorithm to Null Bertrand Type Curves in Minkowski 3-Space ABSTRACT | FULL TEXT ”. Hacettepe Journal of Mathematics and Statistics 39/4 (April 2010), 555-565.
JAMA
Yildirim M, Ilarslan . An Application of Ritt-Wu’s Zero Decomposition Algorithm to Null Bertrand Type Curves in Minkowski 3-Space ABSTRACT | FULL TEXT . Hacettepe Journal of Mathematics and Statistics. 2010;39:555–565.
MLA
Yildirim, Mehmet and kazim Ilarslan. “An Application of Ritt-Wu’s Zero Decomposition Algorithm to Null Bertrand Type Curves in Minkowski 3-Space ABSTRACT | FULL TEXT ”. Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 4, 2010, pp. 555-6.
Vancouver
Yildirim M, Ilarslan . An Application of Ritt-Wu’s Zero Decomposition Algorithm to Null Bertrand Type Curves in Minkowski 3-Space ABSTRACT | FULL TEXT . Hacettepe Journal of Mathematics and Statistics. 2010;39(4):555-6.