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Generalized Quaternions Serret-Frenet and Bishop Frames
Abstract
Serret-Frenet and
Parallel-Transport frame are produced with the help of the generalized
quaternions again by the method in [4].
Keywords
References
- [1] Inoguchi, J., ”Timelike surfaces of constant mean curvature in Minkowski 3- space”, Tokyo J. Math. 21(1) 141-152, 1998.
- [2] Niven, I., ”The roots of a quaternion”, Amer. Math. Monthly 449(6) 386-388, 1942.
- [3] Özdemir, M., Ergin A. A., ”Rotations with timelike quaternions in Minkowski 3-space”, J. Geom. Phys. 56 322-336, 2006
- [4] Hanson, A. J., ”Quaternion Frenet Frames: Making Optimal Tubes and Ribbons from Curves”, Tech. Rep. 407, Indiana Unv. Computer Science Dep., 1994.
- [5] Eisenhart, L. P., ”A Treatise on the Differential Geometry of Curves and Surfaces”, Dover, New York, 1960, Originally published in 1909.
- [6] Flanders, H., Differential Forms with Applications to Physical Sciences”, Academic Press, New York, 1963.
- [7] Gray, A., ”Modern Differential Geometry of Curves and Surfaces”, CRC Press, Inc., Boca Raton, FL, 1993.
- [8] Struik, D. J., ”Lectures on Classical Differential Geometry”, Addison-Wesley, 1961
Details
Primary Language
English
Subjects
Engineering
Journal Section
Research Article
Publication Date
December 12, 2012
Submission Date
August 15, 2012
Acceptance Date
November 15, 2012
Published in Issue
Year 2012 Number: 029
APA
Ata, E., Kemer, Y., & Atasoy, A. (2012). Generalized Quaternions Serret-Frenet and Bishop Frames. Journal of Science and Technology of Dumlupınar University, 029, 29-38. https://izlik.org/JA52UX85AH
AMA
1.Ata E, Kemer Y, Atasoy A. Generalized Quaternions Serret-Frenet and Bishop Frames. DPÜFBED. 2012;(029):29-38. https://izlik.org/JA52UX85AH
Chicago
Ata, Erhan, Yasemin Kemer, and Ali Atasoy. 2012. “Generalized Quaternions Serret-Frenet and Bishop Frames”. Journal of Science and Technology of Dumlupınar University, nos. 029: 29-38. https://izlik.org/JA52UX85AH.
EndNote
Ata E, Kemer Y, Atasoy A (December 1, 2012) Generalized Quaternions Serret-Frenet and Bishop Frames. Journal of Science and Technology of Dumlupınar University 029 29–38.
IEEE
[1]E. Ata, Y. Kemer, and A. Atasoy, “Generalized Quaternions Serret-Frenet and Bishop Frames”, DPÜFBED, no. 029, pp. 29–38, Dec. 2012, [Online]. Available: https://izlik.org/JA52UX85AH
ISNAD
Ata, Erhan - Kemer, Yasemin - Atasoy, Ali. “Generalized Quaternions Serret-Frenet and Bishop Frames”. Journal of Science and Technology of Dumlupınar University. 029 (December 1, 2012): 29-38. https://izlik.org/JA52UX85AH.
JAMA
1.Ata E, Kemer Y, Atasoy A. Generalized Quaternions Serret-Frenet and Bishop Frames. DPÜFBED. 2012;:29–38.
MLA
Ata, Erhan, et al. “Generalized Quaternions Serret-Frenet and Bishop Frames”. Journal of Science and Technology of Dumlupınar University, no. 029, Dec. 2012, pp. 29-38, https://izlik.org/JA52UX85AH.
Vancouver
1.Erhan Ata, Yasemin Kemer, Ali Atasoy. Generalized Quaternions Serret-Frenet and Bishop Frames. DPÜFBED [Internet]. 2012 Dec. 1;(029):29-38. Available from: https://izlik.org/JA52UX85AH