Generalized Quaternions Serret-Frenet and Bishop Frames

Araştırma Makalesi

Yıl 2012, Sayı: 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.

Yıl 2012, Sayı: 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.

Toplam 10 adet kaynakça vardır.

Birincil Dil	İngilizce
Konular	Mühendislik
Bölüm	Makaleler
Yazarlar	Erhan Ata Yasemin Kemer Bu kişi benim Ali Atasoy Bu kişi benim
Yayımlanma Tarihi	12 Aralık 2012
Yayımlandığı Sayı	Yıl 2012 Sayı: 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.