BibTex RIS Cite

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

References

  • 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

References

  • 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.
There are 23 citations in total.

Details

Primary Language Turkish
Journal Section Mathematics
Authors

Mehmet Yildirim This is me

 kazim Ilarslan This is me

Publication Date April 1, 2010
Published in Issue Year 2010 Volume: 39 Issue: 4

Cite

APA 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.