Generalized Quaternions Serret-Frenet and Bishop Frames

Research Article

Year 2012, Issue: 029, 29 - 38, 12.12.2012

Serret-Frenet and
Parallel-Transport frame are produced with the help of the generalized
quaternions again by the method in [4].

[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
[9] Öztürk, U., Hacısalihoğlu, H. H., Yaylı, Y., Koç Öztürk, E. B. ,”Dual Quaternion Frames”, Commun. Fac. Sci. Univ. Ank. Series A1 59(2) 41–50, 2010
[10] Bishop, R. L., ”There is more than one way to frame a curve”, Amer. Math. Monthly 82(3) , 246-251, March 1975.

Year 2012, Issue: 029, 29 - 38, 12.12.2012

Serret-Frenet
ve Paralel taşıma çatıları, genelleştirilmiş kuaterniyonlar yardımıyla yine
[4]te verilen metot ile oluşturulmuştur.

[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
[9] Öztürk, U., Hacısalihoğlu, H. H., Yaylı, Y., Koç Öztürk, E. B. ,”Dual Quaternion Frames”, Commun. Fac. Sci. Univ. Ank. Series A1 59(2) 41–50, 2010
[10] Bishop, R. L., ”There is more than one way to frame a curve”, Amer. Math. Monthly 82(3) , 246-251, March 1975.

There are 10 citations in total.

Primary Language	English
Subjects	Engineering
Journal Section	Articles
Authors	Erhan Ata Yasemin Kemer This is me Ali Atasoy This is me
Publication Date	December 12, 2012
Published in Issue	Year 2012 Issue: 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.

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